Find values for the variables so that the following matrices are equal. X= x 4y 6 Z= Z = (Simplify your answer.) y = (Simplify your answer.) (Simplify your answer.) 18 12 1 6 C...
Find values for the variables so that the following matrices are equal. X= x 4y 6 Z= Z = (Simplify your answer.) y = (Simplify your answer.) (Simplify your answer.) 18 12 1 6 C...
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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![**Problem Statement:**
Find values for the variables so that the following matrices are equal.
\[
\begin{bmatrix}
x & 4y \\
z & 6
\end{bmatrix}
=
\begin{bmatrix}
18 & 12 \\
1 & 6
\end{bmatrix}
\]
**Solution:**
To find the values of variables \( x \), \( y \), and \( z \), equate corresponding elements of the matrices:
1. For the element in the first row and first column:
\[ x = 18 \]
2. For the element in the first row and second column:
\[ 4y = 12 \]
\[ y = \frac{12}{4} = 3 \]
3. For the element in the second row and first column:
\[ z = 1 \]
Given the above equations, we solve for each variable:
**x =** \([18]\) (Simplify your answer.)
**y =** \([3]\) (Simplify your answer.)
**z =** \([1]\) (Simplify your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc29afaca-2bcc-449e-b541-aa3eef827b4a%2F16464a4d-a232-4924-9d7d-3b276a884897%2F5yu93tn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find values for the variables so that the following matrices are equal.
\[
\begin{bmatrix}
x & 4y \\
z & 6
\end{bmatrix}
=
\begin{bmatrix}
18 & 12 \\
1 & 6
\end{bmatrix}
\]
**Solution:**
To find the values of variables \( x \), \( y \), and \( z \), equate corresponding elements of the matrices:
1. For the element in the first row and first column:
\[ x = 18 \]
2. For the element in the first row and second column:
\[ 4y = 12 \]
\[ y = \frac{12}{4} = 3 \]
3. For the element in the second row and first column:
\[ z = 1 \]
Given the above equations, we solve for each variable:
**x =** \([18]\) (Simplify your answer.)
**y =** \([3]\) (Simplify your answer.)
**z =** \([1]\) (Simplify your answer.)
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