Matrix A = (3 x 3) Row 1 is: 5 -2 2 Row 2 is: 0 3 -3 row 3 is: 2 -4 7 part ii) Using Cramer’s rule (please compute all the required determinants) to find x3 component of the solution to: Ax = (3 x 1) Row 1 is: 0 Row 2 is: 1 Row 3 is: 0 What is this value in determines of A−1 ? May you please througougly go through your steps using Cramer's rule, as it is extrememly confusing to me part iii) Consider now (n×n) matrices A, B. Let P be an invertible (n×n) matrix such that: P-1 AP= B. Derive: det(A) = det(B) please look at picture
Matrix A = (3 x 3) Row 1 is: 5 -2 2 Row 2 is: 0 3 -3 row 3 is: 2 -4 7 part ii) Using Cramer’s rule (please compute all the required determinants) to find x3 component of the solution to: Ax = (3 x 1) Row 1 is: 0 Row 2 is: 1 Row 3 is: 0 What is this value in determines of A−1 ? May you please througougly go through your steps using Cramer's rule, as it is extrememly confusing to me part iii) Consider now (n×n) matrices A, B. Let P be an invertible (n×n) matrix such that: P-1 AP= B. Derive: det(A) = det(B) please look at picture
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Matrix A = (3 x 3)
Row 1 is: 5 -2 2
Row 2 is: 0 3 -3
row 3 is: 2 -4 7
part ii) Using Cramer’s rule (please compute all the required determinants) to find x3 component of the solution to:
Ax = (3 x 1)
Row 1 is: 0
Row 2 is: 1
Row 3 is: 0
What is this value in determines of A−1 ?
May you please througougly go through your steps using Cramer's rule, as it is extrememly confusing to me
part iii) Consider now (n×n) matrices A, B. Let P be an invertible (n×n) matrix such that:
P-1 AP= B.
Derive: det(A) = det(B)
please look at picture

Transcribed Image Text:Problem 4
Consider the matrix
5 -2
2
А
3 -3
2 -4
(i) Compute the determinant of A by taking the cofactor expansion along the second row.
(ii) Using Cramer's rule (please compute all the required determinants) to find x3 com-
ponent of the solution to
Ах
What is this value in determines of A-1? NO CREDIT WILL BE GIVEN IF
CRAMER'S METHOD IS NOT USED.
(iii) Consider now (n x n) matrices A, B. Let P be an invertible (n x n) matrix such that
P-'AP = B.
Derive
det (A) = det(B).
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