6. Consider the matrix A-41 A = (a) Find the determinant of A. (b) Give a one sentence reason why A-1 exists and then find A-¹. (c) Give an example of a 2x2 matrix B where all it's elements are distinct (i.e. different) numbers and B-1 does not exist. Give a one sentence reason why your B-1 does not exist.
6. Consider the matrix A-41 A = (a) Find the determinant of A. (b) Give a one sentence reason why A-1 exists and then find A-¹. (c) Give an example of a 2x2 matrix B where all it's elements are distinct (i.e. different) numbers and B-1 does not exist. Give a one sentence reason why your B-1 does not exist.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![6. Consider the matrix
\[ A = \begin{bmatrix} 4 & 1 \\ -1 & 7 \end{bmatrix} \]
(a) Find the determinant of \( A \).
(b) Give a one sentence reason why \( A^{-1} \) exists and then find \( A^{-1} \).
(c) Give an example of a 2x2 matrix \( B \) where all its elements are distinct (i.e. different) numbers and \( B^{-1} \) does not exist. Give a one sentence reason why your \( B^{-1} \) does not exist.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1c03a31-30c3-4bf6-813c-be7cccb63124%2F9a5432fd-5b95-4a09-9718-8392769cec57%2Flqycjgr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. Consider the matrix
\[ A = \begin{bmatrix} 4 & 1 \\ -1 & 7 \end{bmatrix} \]
(a) Find the determinant of \( A \).
(b) Give a one sentence reason why \( A^{-1} \) exists and then find \( A^{-1} \).
(c) Give an example of a 2x2 matrix \( B \) where all its elements are distinct (i.e. different) numbers and \( B^{-1} \) does not exist. Give a one sentence reason why your \( B^{-1} \) does not exist.
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