Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
5th Edition
ISBN: 9780134689531
Author: Lee Johnson, Dean Riess, Jimmy Arnold
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 4.2, Problem 10E
To determine
To calculate:
The determinant of the matrix
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
a
Question 7. If det d e f
ghi
V3
= 2. Find det
-1
2
Question 8. Let A = 1
4
5
0
3
2.
1 Find adj (A)
2 Find det (A)
3
Find A-1
2g 2h 2i
-e-f
-d
273
2a 2b 2c
Question 1. Solve the system
-
x1 x2 + 3x3 + 2x4
-x1 + x22x3 + x4
2x12x2+7x3+7x4
Question 2. Consider the system
= 1
=-2
= 1
3x1 - x2 + ax3
= 1
x1 + 3x2 + 2x3
x12x2+2x3
= -b
= 4
1 For what values of a, b will the system be inconsistent?
2 For what values of a, b will the system have only one solution?
For what values of a, b will the saystem have infinitely many solutions?
Question 5. Let A, B, C ben x n-matrices, S is nonsigular. If A = S-1 BS, show that
det (A) = det (B)
Question 6. For what values of k is the matrix A = (2- k
-1
-1
2) singular?
k
Chapter 4 Solutions
Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...
Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - In Exercises 1-12, find the eigenvalues and the...Ch. 4.1 - Using Eq.4, apply the singularity test to the...Ch. 4.1 - Using Eq.4, apply the singularity test to the...Ch. 4.1 - Using Eq.4, apply the singularity test to the...Ch. 4.1 - Using Eq.4, apply the singularity test to the...Ch. 4.1 - Consider the (22) symmetric matrix A=[abbd]. Show...Ch. 4.1 - Consider the (22) matrix A given by A=[abba],b0....Ch. 4.1 - Let A be a (22) matrix. Show that A and AT have...Ch. 4.2 - In Exercises 1-6, list the minor matrix Mij, and...Ch. 4.2 - In Exercises 1-6, list the minor matrix Mij, and...Ch. 4.2 - Prob. 3ECh. 4.2 - In Exercises 1-6, list the minor matrix Mij, and...Ch. 4.2 - Prob. 5ECh. 4.2 - In Exercises 1-6, list the minor matrix Mij, and...Ch. 4.2 - Prob. 7ECh. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - In Exercises 8-19, calculate the determinant of...Ch. 4.2 - Prob. 13ECh. 4.2 - In Exercises 8-19, calculate the determinant of...Ch. 4.2 - In Exercises 8-19, calculate the determinant of...Ch. 4.2 - In Exercises 8-19, calculate the determinant of...Ch. 4.2 - Prob. 17ECh. 4.2 - In Exercises 8-19, calculate the determinant of...Ch. 4.2 - Prob. 19ECh. 4.2 - Let A=(aij) be a given (33) matrix. Form the...Ch. 4.2 - In Exercises 21 and 22, find all ordered pairs...Ch. 4.2 - In Exercises 21 and 22, find all ordered pairs...Ch. 4.2 - Let A=(aij) be the (nn) matrix specified thus:...Ch. 4.2 - Let A and B be (nn) matrices. Use Theorems 2 and 3...Ch. 4.2 - Suppose that A is a (nn) nonsingular matrix, and...Ch. 4.2 - Prob. 26ECh. 4.2 - In Exercises 27-30, use Theorem 2 and Exercise 25...Ch. 4.2 - In Exercises 27-30, use Theorem 2 and Exercise 25...Ch. 4.2 - In Exercises 27-30, use Theorem 2 and Exercise 25...Ch. 4.2 - In Exercises 27-30, use Theorem 2 and Exercise 25...Ch. 4.2 - a Let A be an (nn) matrix. If n=3, det(A) can be...Ch. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.3 - In Exercise 1-6, evaluate det(A) by using row...Ch. 4.3 - In Exercise 1-6, evaluate det(A) by using row...Ch. 4.3 - Prob. 3ECh. 4.3 - In Exercise 1-6, evaluate det(A) by using row...Ch. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - In Exercise 7-12, use only column interchanges or...Ch. 4.3 - Prob. 9ECh. 4.3 - In Exercise 7-12, use only column interchanges or...Ch. 4.3 - In Exercise 7-12, use only column interchanges or...Ch. 4.3 - Prob. 12ECh. 4.3 - In Exercise 13-18, assume that the (33) matrix A...Ch. 4.3 - In Exercise 13-18, assume that the (33) matrix A...Ch. 4.3 - In Exercise 13-18, assume that the (33) matrix A...Ch. 4.3 - In Exercise 13-18, assume that the (33) matrix A...Ch. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - In Exercise 19-22, evaluate the (44) determinants....Ch. 4.3 - In Exercise 19-22, evaluate the (44) determinants....Ch. 4.3 - In Exercise 19-22, evaluate the (44) determinants....Ch. 4.3 - In Exercise 19-22, evaluate the (44) determinants....Ch. 4.3 - In Exercise 23 and 24, use row operations to...Ch. 4.3 - In Exercise 23 and 24, use row operations to...Ch. 4.3 - Let A be a (nn) matrix. Use Theorem 7 to argue...Ch. 4.3 - Prove the corollary to Theorem 6. Hint: Suppose...Ch. 4.3 - Find examples of (22) matrices A and B such that...Ch. 4.3 - An (nn) matrix A is called skew symmetric if AT=A....Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - In Exercises 1 14, find the characteristic...Ch. 4.4 - Prove property b of theorem 11. Hint: Begin with...Ch. 4.4 - Prove property c of Theorem 11. Theorem 11 Let A...Ch. 4.4 - Complete the proof of property a of Theorem 11....Ch. 4.4 - Let qt=t3-2t2-t+2; and for any nn matrix H, define...Ch. 4.4 - With qt as in Exercise 18, verify that qC is the...Ch. 4.4 - Exercises 20 23 illustrate the Cayley-Hamilton...Ch. 4.4 - Exercises 20 23 illustrate the Cayley-Hamilton...Ch. 4.4 - Exercises 20 23 illustrate the Cayley-Hamilton...Ch. 4.4 - Exercises 20 23 illustrate the Cayley-Hamilton...Ch. 4.4 - This problem establishes a special case of the...Ch. 4.4 - Consider the 22 matrix A given by A=abcd. The...Ch. 4.4 - Prob. 26ECh. 4.4 - Let qt=tn+an-1tn-1++a1t+a0, and define the nn...Ch. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - Prob. 34ECh. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - The following list of matrices and their...Ch. 4.5 - In Exercise 12-17, find the eigenvalues and the...Ch. 4.5 - In Exercise 12-17, find the eigenvalues and the...Ch. 4.5 - In Exercise 12-17, find the eigenvalues and the...Ch. 4.5 - In Exercise 12-17, find the eigenvalues and the...Ch. 4.5 - In Exercise 12-17, find the eigenvalues and the...Ch. 4.5 - In Exercise 12-17, find the eigenvalues and the...Ch. 4.5 - If a vector x is a linear combination of...Ch. 4.5 - As in Exercise 18, calculate A10x for...Ch. 4.5 - Consider a (44) matrix H of the form...Ch. 4.5 - An (nn) matrix P is called idempotent if P2=P....Ch. 4.5 - Let P be an idempotent matrix. Show that the only...Ch. 4.5 - Let u be a vector in Rn such that uTu=1. Show that...Ch. 4.5 - Verify that if Q is idempotent, then so is IQ....Ch. 4.5 - Suppose that u and v are vectors in Rn such that...Ch. 4.5 - Show that any nonzero vector of the form au+bv is...Ch. 4.5 - Prob. 27ECh. 4.5 - Let A be a symmetric matrix and suppose that Au=u,...Ch. 4.5 - Prob. 29ECh. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - Prob. 2ECh. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - In Exercises 1-18, s=1+2i,u=32i,v=4+i,w=2i, and...Ch. 4.6 - Prob. 18ECh. 4.6 - Find the eigenvalues and the eigenvectors for the...Ch. 4.6 - Find the eigenvalues and the eigenvectors for the...Ch. 4.6 - Find the eigenvalues and the eigenvectors for the...Ch. 4.6 - Find the eigenvalues and the eigenvectors for the...Ch. 4.6 - Find the eigenvalues and the eigenvectors for the...Ch. 4.6 - Find the eigenvalues and the eigenvectors for the...Ch. 4.6 - In Exercises 25 and 26, solve the linear system....Ch. 4.6 - In Exercises 25 and 26, solve the linear system....Ch. 4.6 - In Exercises 27-30, calculate x. x=[1+i2]Ch. 4.6 - In Exercises 27-30, calculate x. x=[3+i2i]Ch. 4.6 - In Exercises 27-30, calculate x. x=[12ii3+i]Ch. 4.6 - In Exercises 27-30, calculate x. x=[2i1i3]Ch. 4.6 - Prob. 31ECh. 4.6 - In Exercises 31-34, use linear algebra software to...Ch. 4.6 - Prob. 33ECh. 4.6 - Prob. 34ECh. 4.6 - Establish the five properties of the conjugate...Ch. 4.6 - Let A be an (mn) matrix, and let B be an (np)...Ch. 4.6 - Prob. 37ECh. 4.6 - An (nn) matrix A is called Hermitian if A*=A....Ch. 4.6 - Let p(t)=a0+a1t+...+antn, where the coefficients...Ch. 4.6 - Prob. 40ECh. 4.6 - A real symmetric (nn) matrix A is called positive...Ch. 4.6 - An (nn) matrix A is called unitary if A*A=I. If A...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 1 12, determine whether the given...Ch. 4.7 - In Exercises 13 18, use condition 5 to determine...Ch. 4.7 - In Exercises 13 18, use condition 5 to determine...Ch. 4.7 - In Exercises 13 18, use condition 5 to determine...Ch. 4.7 - In Exercises 13 18, use condition 5 to determine...Ch. 4.7 - In Exercises 13 18, use condition 5 to determine...Ch. 4.7 - In Exercises 13 18, use condition 5 to determine...Ch. 4.7 - In Exercises 19 and 20, find values ,,a,bandc such...Ch. 4.7 - In Exercises 19 and 20, find values ,,a,bandc such...Ch. 4.7 - Let A be an (nn) matrix, and let S be a...Ch. 4.7 - Show that if A is diagonalizable and if B is...Ch. 4.7 - Suppose that B is similar to A. Show each of the...Ch. 4.7 - Prove properties b and c of Theorem 21. Hint: For...Ch. 4.7 - Let u be a vector in Rn such that uTu=1. Let...Ch. 4.7 - Suppose that A and B are orthogonal (nn) matrices....Ch. 4.7 - Prob. 31ECh. 4.7 - Prob. 32ECh. 4.7 - Prob. 33ECh. 4.7 - Prob. 34ECh. 4.7 - Prob. 35ECh. 4.7 - Prob. 36ECh. 4.7 - Prob. 37ECh. 4.7 - Prob. 38ECh. 4.7 - Let B=QTAQ, where q and A are as in Exercise 38....Ch. 4.7 - Prob. 40ECh. 4.7 - Following the outline of Exercises 38-40, use...Ch. 4.7 - Consider the (nn) symmetric matrix A=(aij) defined...Ch. 4.7 - Suppose that A is a real symmetric matrix and that...Ch. 4.8 - In Exercises 1-6, consider the vector sequence...Ch. 4.8 - Prob. 2ECh. 4.8 - In Exercises 1-6, consider the vector sequence...Ch. 4.8 - Prob. 4ECh. 4.8 - In Exercises 1-6, consider the vector sequence...Ch. 4.8 - Prob. 6ECh. 4.8 - In Exercises 7-14, let xk=Axk1, k=1,2,....... for...Ch. 4.8 - Prob. 8ECh. 4.8 - In Exercises 7-14, let xk=Axk1, k=1,2,....... for...Ch. 4.8 - Prob. 10ECh. 4.8 - In Exercises 7-14, let xk=Axk1, k=1,2,, for the...Ch. 4.8 - Prob. 12ECh. 4.8 - Prob. 13ECh. 4.8 - Prob. 14ECh. 4.8 - Prob. 15ECh. 4.8 - In Exercises 15-18, solve the initial-value...Ch. 4.8 - Prob. 17ECh. 4.8 - Prob. 18ECh. 4.8 - Prob. 19ECh. 4.8 - Prob. 20ECh. 4.8 - Prob. 21ECh. 4.8 - Prob. 22ECh. 4.8 - Prob. 23ECh. 4.8 - Prob. 24ECh. 4.8 - Prob. 25ECh. 4.8 - Prob. 26ECh. 4.8 - Prob. 27ECh. 4.8 - Prob. 28ECh. 4.8 - Prob. 29ECh. 4.SE - Prob. 1SECh. 4.SE - Prob. 2SECh. 4.SE - Prob. 3SECh. 4.SE - Prob. 4SECh. 4.SE - Prob. 5SECh. 4.SE - Prob. 6SECh. 4.SE - Prob. 7SECh. 4.SE - Prob. 8SECh. 4.SE - Prob. 9SECh. 4.SE - Prob. 10SECh. 4.SE - Prob. 11SECh. 4.SE - Prob. 12SECh. 4.SE - Prob. 13SECh. 4.SE - Prob. 14SECh. 4.CE - CONCEPTUAL EXERCISES In Exercises 18, answer true...Ch. 4.CE - Prob. 2CECh. 4.CE - CONCEPTUAL EXERCISES In Exercises 18, answer true...Ch. 4.CE - Prob. 4CECh. 4.CE - Prob. 5CECh. 4.CE - Prob. 6CECh. 4.CE - Prob. 7CECh. 4.CE - CONCEPTUAL EXERCISES In Exercises 18, answer true...Ch. 4.CE - Prob. 9CECh. 4.CE - In Exercises 9-14, give a brief answer. Suppose...Ch. 4.CE - In Exercises 9-14, give a brief answer. Show that...Ch. 4.CE - In Exercises 9-14, give a brief answer. Let A and...Ch. 4.CE - Prob. 13CECh. 4.CE - In Exercises 9-14, give a brief answer. Let u be a...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- 1 4 5 Question 3. Find A-1 (if exists), where A = -3 -1 -2 2 3 4 Question 4. State 4 equivalent conditions for a matrix A to be nonsingulararrow_forwardHow long is a guy wire reaching from the top of a 15-foot pole to a point on the ground 9-feet from the pole? Question content area bottom Part 1 The guy wire is exactly feet long. (Type an exact answer, using radicals as needed.) Part 2 The guy wire is approximatelyfeet long. (Round to the nearest thousandth.)arrow_forwardQuestion 6 Not yet answered Marked out of 5.00 Flag question = If (4,6,-11) and (-12,-16,4), = Compute the cross product vx w karrow_forward
- Consider the following vector field v^-> (x,y): v^->(x,y)=2yi−xj What is the magnitude of the vector v⃗ located in point (13,9)? [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places]arrow_forwardQuestion 4 Find the value of the first element for the first row of the inverse matrix of matrix B. 3 Not yet answered B = Marked out of 5.00 · (³ ;) Flag question 7 [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places] Answer:arrow_forwardQuestion 2 Not yet answered Multiply the following Matrices together: [77-4 A = 36 Marked out of -5 -5 5.00 B = 3 5 Flag question -6 -7 ABarrow_forward
- Assume {u1, U2, u3, u4} does not span R³. Select the best statement. A. {u1, U2, u3} spans R³ if u̸4 is a linear combination of other vectors in the set. B. We do not have sufficient information to determine whether {u₁, u2, u3} spans R³. C. {U1, U2, u3} spans R³ if u̸4 is a scalar multiple of another vector in the set. D. {u1, U2, u3} cannot span R³. E. {U1, U2, u3} spans R³ if u̸4 is the zero vector. F. none of the abovearrow_forwardSelect the best statement. A. If a set of vectors includes the zero vector 0, then the set of vectors can span R^ as long as the other vectors are distinct. n B. If a set of vectors includes the zero vector 0, then the set of vectors spans R precisely when the set with 0 excluded spans Rª. ○ C. If a set of vectors includes the zero vector 0, then the set of vectors can span Rn as long as it contains n vectors. ○ D. If a set of vectors includes the zero vector 0, then there is no reasonable way to determine if the set of vectors spans Rn. E. If a set of vectors includes the zero vector 0, then the set of vectors cannot span Rn. F. none of the abovearrow_forwardWhich of the following sets of vectors are linearly independent? (Check the boxes for linearly independent sets.) ☐ A. { 7 4 3 13 -9 8 -17 7 ☐ B. 0 -8 3 ☐ C. 0 ☐ D. -5 ☐ E. 3 ☐ F. 4 THarrow_forward
- 3 and = 5 3 ---8--8--8 Let = 3 U2 = 1 Select all of the vectors that are in the span of {u₁, u2, u3}. (Check every statement that is correct.) 3 ☐ A. The vector 3 is in the span. -1 3 ☐ B. The vector -5 75°1 is in the span. ГОЛ ☐ C. The vector 0 is in the span. 3 -4 is in the span. OD. The vector 0 3 ☐ E. All vectors in R³ are in the span. 3 F. The vector 9 -4 5 3 is in the span. 0 ☐ G. We cannot tell which vectors are i the span.arrow_forward(20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0; y₁ = e*, y2 = e¯x, y3 = e−2x (20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y"-2y-3y = 6; y(0) = 3, y'(0) = 11 yc = c₁ex + c2e³x; yp = −2 (60 p) 3. Find the general, and if possible, particular solutions of the linear systems of differential equations given below using the eigenvalue-eigenvector method. (See Section 7.3 in your textbook if you need a review of the subject.) = a) x 4x1 + x2, x2 = 6x1-x2 b) x=6x17x2, x2 = x1-2x2 c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0arrow_forwardFind the perimeter and areaarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
HOW TO FIND DETERMINANT OF 2X2 & 3X3 MATRICES?/MATRICES AND DETERMINANTS CLASS XII 12 CBSE; Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=bnaKGsLYJvQ;License: Standard YouTube License, CC-BY
What are Determinants? Mathematics; Author: Edmerls;https://www.youtube.com/watch?v=v4_dxD4jpgM;License: Standard YouTube License, CC-BY