onsider the matrices A, B, C, and D below. -2 6 1 1 A = 4 4 4 C -8 -6 -2 D = -5 -5 7 -7 -6 -6 -7 -4 ) What are the dimensions of the matrix 6B? 2 X 2 ) What are the dimensions of the matrix DB? 3 X 2 ) What are the dimensions of the matrix CDA? 3 2 ..
onsider the matrices A, B, C, and D below. -2 6 1 1 A = 4 4 4 C -8 -6 -2 D = -5 -5 7 -7 -6 -6 -7 -4 ) What are the dimensions of the matrix 6B? 2 X 2 ) What are the dimensions of the matrix DB? 3 X 2 ) What are the dimensions of the matrix CDA? 3 2 ..
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
![**Part 1**
Consider the matrices \( A, B, C, \) and \( D \) below.
\[
A = \begin{bmatrix} 1 & 4 \\ -5 & 7 \end{bmatrix}, \quad
B = \begin{bmatrix} 4 & 4 \\ -7 & -6 \end{bmatrix}, \quad
C = \begin{bmatrix} -2 & 6 & 1 \\ -8 & -6 & -2 \\ -6 & -7 & -4 \end{bmatrix}, \quad
D = \begin{bmatrix} 5 & 7 \\ -5 & -8 \\ 2 & -2 \end{bmatrix}
\]
1. What are the dimensions of the matrix \( 6B \)?
Answer: \( 2 \times 2 \)
2. What are the dimensions of the matrix \( DB \)?
Answer: \( 3 \times 2 \)
3. What are the dimensions of the matrix \( CDA \)?
Answer: \( 3 \times 2 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F603fbc9e-cdba-4fa0-b3dd-1f2ec72dd924%2F22458b44-a487-473b-acb7-00cc8aa644df%2F3x881fb_processed.png&w=3840&q=75)
Transcribed Image Text:**Part 1**
Consider the matrices \( A, B, C, \) and \( D \) below.
\[
A = \begin{bmatrix} 1 & 4 \\ -5 & 7 \end{bmatrix}, \quad
B = \begin{bmatrix} 4 & 4 \\ -7 & -6 \end{bmatrix}, \quad
C = \begin{bmatrix} -2 & 6 & 1 \\ -8 & -6 & -2 \\ -6 & -7 & -4 \end{bmatrix}, \quad
D = \begin{bmatrix} 5 & 7 \\ -5 & -8 \\ 2 & -2 \end{bmatrix}
\]
1. What are the dimensions of the matrix \( 6B \)?
Answer: \( 2 \times 2 \)
2. What are the dimensions of the matrix \( DB \)?
Answer: \( 3 \times 2 \)
3. What are the dimensions of the matrix \( CDA \)?
Answer: \( 3 \times 2 \)
![### Matrices in Linear Algebra
This section explains the representation of certain matrix expressions, focusing on operations with matrices.
#### Matrix Representations:
1. **Matrix for \(6B\):**
\[
6B = \begin{bmatrix}
24 & 24 \\
-42 & -36
\end{bmatrix}
\]
This matrix shows the result of a scalar multiplication of a matrix \(B\) by 6, where each element of matrix \(B\) has been multiplied by the scalar value.
2. **Matrix for \(DB\):**
\[
DB = \begin{bmatrix}
-29 & -22 \\
36 & 28 \\
22 & 20
\end{bmatrix}
\]
This is a product of two matrices, \(D\) and \(B\). The elements are calculated through the dot products of the rows of \(D\) and the columns of \(B\).
3. **Matrix for \(CDA\):**
\[
CDA = \begin{bmatrix}
150 & 264 \\
6 & 168 \\
113 & 24
\end{bmatrix}
\]
This matrix represents the result of multiplying three matrices: \(C\), \(D\), and \(A\). The multiplication is carried out in sequence, respecting the associative property of matrix multiplication.
These matrices illustrate basic operations in linear algebra, emphasizing the importance of scalar, dot product, and matrix multiplication.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F603fbc9e-cdba-4fa0-b3dd-1f2ec72dd924%2F22458b44-a487-473b-acb7-00cc8aa644df%2F3nci17l_processed.png&w=3840&q=75)
Transcribed Image Text:### Matrices in Linear Algebra
This section explains the representation of certain matrix expressions, focusing on operations with matrices.
#### Matrix Representations:
1. **Matrix for \(6B\):**
\[
6B = \begin{bmatrix}
24 & 24 \\
-42 & -36
\end{bmatrix}
\]
This matrix shows the result of a scalar multiplication of a matrix \(B\) by 6, where each element of matrix \(B\) has been multiplied by the scalar value.
2. **Matrix for \(DB\):**
\[
DB = \begin{bmatrix}
-29 & -22 \\
36 & 28 \\
22 & 20
\end{bmatrix}
\]
This is a product of two matrices, \(D\) and \(B\). The elements are calculated through the dot products of the rows of \(D\) and the columns of \(B\).
3. **Matrix for \(CDA\):**
\[
CDA = \begin{bmatrix}
150 & 264 \\
6 & 168 \\
113 & 24
\end{bmatrix}
\]
This matrix represents the result of multiplying three matrices: \(C\), \(D\), and \(A\). The multiplication is carried out in sequence, respecting the associative property of matrix multiplication.
These matrices illustrate basic operations in linear algebra, emphasizing the importance of scalar, dot product, and matrix multiplication.
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