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Consider the matrix A = | 0 2 (1 1 1 (a) Compute the determinant of A by expanding along the second row. (b) Is A invertible? If it is, give the determinant of the inverse of A/ (c) Without doing any computation, write the reduced echelon form of A. (d) Consider the system of linear equations Ax = b. Without actually computing the solutior of the system, can you say how many solution the system Ax = b has? (e) Let B = 5A. What is the determinant of B? (f) Assume that C is a 3 × 3 matrix of determinant –3, what is the determinant of AC?

Consider the matrix A = | 0 2 (1 1 1 (a) Compute the determinant of A by expanding along the second row. (b) Is A invertible? If it is, give the determinant of the inverse of A/ (c) Without doing any computation, write the reduced echelon form of A. (d) Consider the system of linear equations Ax = b. Without actually computing the solutior of the system, can you say how many solution the system Ax = b has? (e) Let B = 5A. What is the determinant of B? (f) Assume that C is a 3 × 3 matrix of determinant –3, what is the determinant of AC?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2 1 -1 0 2 1 1 2. Consider the matrix A = 1 (a) Compute the determinant of A by expanding along the second row. (b) Is A invertible? If it is, give the determinant of the inverse of A/ (c) Without doing any computation, write the reduced echelon form of A. (d) Consider the system of linear equations Ax = b. Without actually computing the solutions of the system, can you say how many solution the system Ax = b has? (e) Let B = 5A. What is the determinant of B? (f) Assume that C is a 3 x 3 matrix of determinant –3, what is the determinant of AC?
Transcribed Image Text:2 1 -1 0 2 1 1 2. Consider the matrix A = 1 (a) Compute the determinant of A by expanding along the second row. (b) Is A invertible? If it is, give the determinant of the inverse of A/ (c) Without doing any computation, write the reduced echelon form of A. (d) Consider the system of linear equations Ax = b. Without actually computing the solutions of the system, can you say how many solution the system Ax = b has? (e) Let B = 5A. What is the determinant of B? (f) Assume that C is a 3 x 3 matrix of determinant –3, what is the determinant of AC?
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