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 17E
To determine
Whether the given matrix is singular or nonsingular and find
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Find a 2x2 matrix A such that A² = 1
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Find A when (34)¯¹ :
23
3. Illustrate the Gersgorin theorem by the matrix
1
2
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1+ 2i
A =
-1
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-2 – 2i
- -N
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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- 7. Invert the following matrix 3x – 2y = 9 -x + 3y = 3 |arrow_forwardQuestion 1 Set up the relevant matrices and determine the definiteness of the following quadratic forms: 1.1 Q(x1, x2) = xỉ + 2x1x2 – 8x, subject to x1 + x2 = 0. 1.2 Q(11, x2, 23, X4, 13) = 2x² + 4x3 + až + 3xž.arrow_forward4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x? + 2y2 + 2z? – 2xy – 2xz – 2yz, and classify it.arrow_forward
- 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)" = BTATarrow_forward1.3.5 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?arrow_forward• The Matrix B from 3 x 2 at by = 1- is ro 1. 3. 4. 1arrow_forward
- 1. Let a = (5, –8,0, 3) and b = (0, 2, –4, 3). (a) Calculate (2b – 4a) (b) Calculate (2b — 4а) (b + 2а) (c) Calculate || a || and || b || (d) Show that the Triangle Inequality applies in this case. 2. Consider the following matrix: -2 1 3 A = 4. 1 -2 -1 (a) Calculate the determinant of A. (b) Find the inverse of A, if it exists. 3. Solve the following system of linear equations using matrix inversion: -2x + y + 3z = 11 4л + 5у + 32 %3 3 I - 2y – z = -6arrow_forwardIn Problems 13–16, use the following matrices to compute each expression.arrow_forward16. Assume x E R. Give the matrix associated with the quadratic form 3(x,)? + 4(x2)2 – 2x,x2 + 3x1X3 – X,X3. |arrow_forward
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