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

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter6: Matrices And Determinants

Section6.2: The Algebra Of Matrices

Problem 61E

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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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