Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Chapter 8.6, Problem 26E
To determine
The inverse matrix
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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
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?
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- 13. 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_forward3. Illustrate the Gersgorin theorem by the matrix 1 2 | 1+ 2i A = -1 1 -2 – 2i - -Narrow_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
- 1. 2. Find a 2x2 matrix A such that A² = 1 4 -1 Find A when (34)¯¹ : 23arrow_forward5. Suppose that A is an invertible n xn matrix with inverse A-1. Show that det (A) is nonzero and det (A)- = det (A-1).arrow_forward11 Use the Gauss–Jordan method to find the inverse of the [1 0 2] matrix 0 1 L0 1 1]arrow_forward
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