Differential Equations with Boundary-Value Problems (MindTap Course List)
9th Edition
ISBN: 9781305965799
Author: Dennis G. Zill
Publisher: Cengage Learning
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Chapter B, Problem 43E
To determine
The inverse matrix
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7.
Invert the following matrix
3x – 2y = 9
-x + 3y = 3
|
1.3.5 Write f= x + 10x,x2 + x as a difference of squares, and f= xí+ 10x1x2 + 30x as
a sum of squares. What symmetric matrices correspond to these quadratic forms by f
= x' Ax?
Properties of the Transpose In Problems 39–42, either prove
the properties in general using the fact that [ a, ]T = [a, ).
or demonstrate the properties for general 3 × 3 matrices.
39. (A")T = A
40. (A + B)T = AT + BT
41. (kA) = kAT, for any scalar k
42. (AB)" = BTAT
Chapter B Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
Ch. B - Prob. 1ECh. B - Prob. 2ECh. B - Prob. 3ECh. B - Prob. 4ECh. B - Prob. 5ECh. B - Prob. 6ECh. B - Prob. 7ECh. B - Prob. 8ECh. B - Prob. 9ECh. B - Prob. 10E
Ch. B - Prob. 11ECh. B - Prob. 12ECh. B - Prob. 13ECh. B - Prob. 14ECh. B - In Problems 1522 determine whether the given...Ch. B - Prob. 16ECh. B - Prob. 17ECh. B - Prob. 18ECh. B - Prob. 19ECh. B - Prob. 20ECh. B - Prob. 21ECh. B - In Problems 1522 determine whether the given...Ch. B - Prob. 23ECh. B - Prob. 24ECh. B - Prob. 25ECh. B - Prob. 26ECh. B - Prob. 27ECh. B - Prob. 28ECh. B - Prob. 29ECh. B - Prob. 30ECh. B - Prob. 31ECh. B - Prob. 32ECh. B - Prob. 33ECh. B - Prob. 34ECh. B - Prob. 35ECh. B - Prob. 36ECh. B - Prob. 37ECh. B - Prob. 38ECh. B - Prob. 39ECh. B - Prob. 40ECh. B - Prob. 41ECh. B - Prob. 42ECh. B - Prob. 43ECh. B - Prob. 44ECh. B - Prob. 45ECh. B - Prob. 46ECh. B - Prob. 47ECh. B - Prob. 48ECh. B - Prob. 49ECh. B - Prob. 50ECh. B - Prob. 51ECh. B - Prob. 52ECh. B - Prob. 53ECh. B - Prob. 54ECh. B - Prob. 55ECh. B - Prob. 56ECh. B - Prob. 57ECh. B - Prob. 58ECh. B - Prob. 59ECh. B - Prob. 60ECh. B - Prob. 61ECh. B - Prob. 62E
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- 3. Illustrate the Gersgorin theorem by the matrix 1 2 | 1+ 2i A = -1 1 -2 – 2i - -Narrow_forward13. Find the inverse of the matrix * 1 2 3 A -2 -2 || 5 A : 10 1 A : 1 4 1 1 10 - 10 -10 -8 -5 -1 1 1 O A = |0 - -/5arrow_forwardHELP WITH 18 AND 19 In each of Problems 12–23, find AR and produce a matrix 2r such that QRA = AR. -1 4 2 3 -5 7 1 18. A = 1 -3 4 4 19. A = 0 0 0arrow_forward
- 5.3 Use the adjoint method to determine the inverse of the coefficient matrix given by [2 3 1] A=3 4 1 13 7 2.arrow_forward4. If G is a 3 x 1 matrix while H is a 1 x 3 matrix then A. GH is 3 x 3, HG is 1 x 1. B. GH is 1 x 1, HG is 3 x 3. C. GH is 3 x 3, HG is undefined. D. GH is undefined, HG is 1 x 1. 1 5. What is the inverse of I =| 2 1 1? |2 2 3 1 1 1 A. I' does not exist. C.2 1 -1 1 1 B.-2 -1 -1 D. 4 -1 4 -2 - 2 - 3 1 2 0 1 3 -7 4 6. Compute for the determinant of J =0 -1 А. -81 В. -45 С. -18 D. 18arrow_forward4. The matrix product 2 0 T 1 5 -1 24 P 0 1arrow_forward
- 11. Any square matrix A with det(A)=-2 has an inverse matrix. True False 12. If * 1 1 + 2a a? – 2 5 a 5 | O a = 1 O a = 3 O a = 2 O a = -1 a = 3, –1,2 Nonearrow_forward3.7. Give examples of matrices A for which the number of solutions for A = b is... (a) 0 or 1, depending on b. (b) 0, no matter what b is. (c) 0 or o, depending on b. (d) 1, no matter what 5 is.arrow_forward4 6 For matrix A = if f(X) = X² – 3X, calculate f(A)? 5/ 22 36 A. ( 22 18 B. \36 28/ \18 28/ (22 C. 18 22 -36 D. 36 28/ -18 28arrow_forward
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