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= [a b] and B =[2³]. a. Compute AB. b. If AB = 1-5₂ 1. Let A = find the entries of A, i.e. find the values of a, b, c, and d.

= [a b] and B =[2³]. a. Compute AB. b. If AB = 1-5₂ 1. Let A = find the entries of A, i.e. find the values of a, b, c, and d.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.1: Matrix Operations
Problem 20EQ: Referring to Exercise 19, suppose that the unit cost of distributing the products to stores is the...
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### Matrix Multiplication Problem 1. Let \( A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \) and \( B = \begin{bmatrix} 7 & 3 \\ 2 & 1 \end{bmatrix} \). a. **Compute \( AB \)**. b. **If \( AB = \begin{bmatrix} 5 & 4 \\ -2 & 3 \end{bmatrix} \)**, find the entries of \( A \), i.e., find the values of \( a, b, c, \) and \( d \). ### Explanation of the Problem - **Matrix \( A \) and Matrix \( B \)**: \( A \) is a 2x2 matrix where \( a, b, c, \) and \( d \) are variables, and \( B \) is a 2x2 matrix with given numerical entries. - **Finding the Product \( AB \)**: To compute the product \( AB \), perform matrix multiplication. - **Determining the Entries of Matrix \( A \)**: Given the resulting product matrix \( AB \), find the values of \( a, b, c, \) and \( d \) that satisfy the equation \( AB = \begin{bmatrix} 5 & 4 \\ -2 & 3 \end{bmatrix} \). For educational purposes, students should review the methods for matrix multiplication and solving systems of linear equations to determine the unknowns in matrix \( A \).
Transcribed Image Text:### Matrix Multiplication Problem 1. Let \( A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \) and \( B = \begin{bmatrix} 7 & 3 \\ 2 & 1 \end{bmatrix} \). a. **Compute \( AB \)**. b. **If \( AB = \begin{bmatrix} 5 & 4 \\ -2 & 3 \end{bmatrix} \)**, find the entries of \( A \), i.e., find the values of \( a, b, c, \) and \( d \). ### Explanation of the Problem - **Matrix \( A \) and Matrix \( B \)**: \( A \) is a 2x2 matrix where \( a, b, c, \) and \( d \) are variables, and \( B \) is a 2x2 matrix with given numerical entries. - **Finding the Product \( AB \)**: To compute the product \( AB \), perform matrix multiplication. - **Determining the Entries of Matrix \( A \)**: Given the resulting product matrix \( AB \), find the values of \( a, b, c, \) and \( d \) that satisfy the equation \( AB = \begin{bmatrix} 5 & 4 \\ -2 & 3 \end{bmatrix} \). For educational purposes, students should review the methods for matrix multiplication and solving systems of linear equations to determine the unknowns in matrix \( A \).
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