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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![**Matrix Equation Problem:**
Solve the matrix equation \( AX = B \) for matrix \( X \).
**Given Matrices:**
Matrix \( A \):
\[
A = \begin{bmatrix} 1 & 1 \\ 4 & 2 \end{bmatrix}
\]
Matrix \( B \):
\[
B = \begin{bmatrix} 2 & 3 \\ 7 & 8 \end{bmatrix}
\]
**Objective:**
Find matrix \( X \).
**Solution:**
To solve the equation \( AX = B \), we need to find the inverse of matrix \( A \), noted as \( A^{-1} \), and use it to solve for \( X \).
\[ X = A^{-1}B \]
**Steps:**
1. Check if \( A \) is invertible by ensuring its determinant is non-zero.
2. Calculate the inverse \( A^{-1} \).
3. Multiply \( A^{-1} \) by \( B \) to find \( X \).
**Note:**
Solve this step-by-step as an exercise to practice matrix operations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81220fef-c28a-4927-81fd-b964930d6471%2F984894b6-a67a-4439-80e1-2279909e51fe%2Fpuzjt0j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Matrix Equation Problem:**
Solve the matrix equation \( AX = B \) for matrix \( X \).
**Given Matrices:**
Matrix \( A \):
\[
A = \begin{bmatrix} 1 & 1 \\ 4 & 2 \end{bmatrix}
\]
Matrix \( B \):
\[
B = \begin{bmatrix} 2 & 3 \\ 7 & 8 \end{bmatrix}
\]
**Objective:**
Find matrix \( X \).
**Solution:**
To solve the equation \( AX = B \), we need to find the inverse of matrix \( A \), noted as \( A^{-1} \), and use it to solve for \( X \).
\[ X = A^{-1}B \]
**Steps:**
1. Check if \( A \) is invertible by ensuring its determinant is non-zero.
2. Calculate the inverse \( A^{-1} \).
3. Multiply \( A^{-1} \) by \( B \) to find \( X \).
**Note:**
Solve this step-by-step as an exercise to practice matrix operations.
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