(a) Let A be the matrix 1 2 0 -1 0 -2 -1 0 A = 4 10 2 -2 -1 5 2 -1 (i) Compute the determinant of the matrix A using cofactor expansion along column 4. (ii) Is the matrix A invertible? Justify your answer. Suppose that P and Q are invertible 2 × 2 matrices such that det (PT) = 2 and det(Q) = -2. Let A = R be a scalar. If det(AP³Q2)=10x-12 what are the possible values of X? Justify your answer.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Hi, can someone please help me solve this question? I have been stuck on it for a while, I especially can't figure out part b, thank you so much!!

(a) Let A be the matrix
1
2
0 -1
0
-2
-1 0
A =
4
10
2 -2
-1
5
2
-1
(i) Compute the determinant of the matrix A using cofactor expansion along column 4.
(ii) Is the matrix A invertible? Justify your answer.
Suppose that P and Q are invertible 2 × 2 matrices such that det (PT) = 2 and det(Q) = -2. Let A = R be a scalar. If
det(AP³Q2)=10x-12
what are the possible values of X? Justify your answer.
Transcribed Image Text:(a) Let A be the matrix 1 2 0 -1 0 -2 -1 0 A = 4 10 2 -2 -1 5 2 -1 (i) Compute the determinant of the matrix A using cofactor expansion along column 4. (ii) Is the matrix A invertible? Justify your answer. Suppose that P and Q are invertible 2 × 2 matrices such that det (PT) = 2 and det(Q) = -2. Let A = R be a scalar. If det(AP³Q2)=10x-12 what are the possible values of X? Justify your answer.
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