Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Matrix Multiplication Problem**
**Objective:**
Find the matrix \( A \) such that:
\[
\begin{bmatrix} 1 & 0 \\ -1 & 9 \end{bmatrix} A = \begin{bmatrix} -1 & -3 \\ 7 & 12 \end{bmatrix}
\]
**Hint:**
Let
\[
A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}
\]
**Problem Overview:**
You are given a matrix multiplication equation involving a 2x2 matrix on the left-hand side and its resultant on the right-hand side. Your task is to determine the unknown matrix \( A \).
### Steps to Solve:
1. Assume matrix \( A \) as a 2x2 matrix with elements \( a, b, c, \) and \( d \).
2. Perform matrix multiplication between the given 2x2 matrix and matrix \( A \).
3. Equate the resulting matrix with the given matrix on the right-hand side to find the values of \( a, b, c, \) and \( d \).
### Educational Focus:
This problem helps in understanding the concept of matrix multiplication and the process of finding an unknown matrix through equation solving.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F815a7b78-47c0-41ac-8363-1babdfb18cdd%2F55b4bf4d-ae76-4910-b739-88143e2cba5f%2Flpn1gr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Matrix Multiplication Problem**
**Objective:**
Find the matrix \( A \) such that:
\[
\begin{bmatrix} 1 & 0 \\ -1 & 9 \end{bmatrix} A = \begin{bmatrix} -1 & -3 \\ 7 & 12 \end{bmatrix}
\]
**Hint:**
Let
\[
A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}
\]
**Problem Overview:**
You are given a matrix multiplication equation involving a 2x2 matrix on the left-hand side and its resultant on the right-hand side. Your task is to determine the unknown matrix \( A \).
### Steps to Solve:
1. Assume matrix \( A \) as a 2x2 matrix with elements \( a, b, c, \) and \( d \).
2. Perform matrix multiplication between the given 2x2 matrix and matrix \( A \).
3. Equate the resulting matrix with the given matrix on the right-hand side to find the values of \( a, b, c, \) and \( d \).
### Educational Focus:
This problem helps in understanding the concept of matrix multiplication and the process of finding an unknown matrix through equation solving.
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