Problem 2 Let A and B be 3 x 3-matrices, with det(A) = -2 and det(B) = 3. (1) Is A invertible? (justify your answer) (2) Is B invertible? (justify your answer) (3) Use properties of determinants to compute: (a) det(AB) (b) det (5A) (c) det(A-1) (d) det(AB-1) (e) det(A3) -17--1

Problem 2 Let A and B be 3 x 3-matrices, with det(A) = -2 and det(B) = 3. (1) Is A invertible? (justify your answer) (2) Is B invertible? (justify your answer) (3) Use properties of determinants to compute: (a) det(AB) (b) det (5A) (c) det(A-1) (d) det(AB-1) (e) det(A3) -17--1

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter10: Matrices

Section10.CR: Chapter 10 Review

Problem 14CR

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Question

Linear algebra! Please solve first 2 part correctly and handwritten

Problem 2 Let A and B be 3 x 3-matrices, with det(A) = -2 and det(B) = 3.
(1) Is A invertible? (justify your answer)
(2) Is B invertible? (justify your answer)
(3) Use properties of determinants to compute:
(a) det(AB)
(b) det (5A)
(c) det(A-1)
(d) det(AB-1)
(e) det(A3)
-17--1

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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