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Find BA. A = BA= -1 - 1 -6-2 B = -2 - 3 -4 -1

Find BA. A = BA= -1 - 1 -6-2 B = -2 - 3 -4 -1

Algebra and Trigonometry (6th Edition)
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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### Matrix Multiplication: Finding BA **Objective:** Calculate the product of matrices B and A (denoted as BA). **Given Matrices:** Matrix \( A \): \[ A = \begin{bmatrix} -1 & -1 \\ -6 & -2 \end{bmatrix} \] Matrix \( B \): \[ B = \begin{bmatrix} -2 & -3 \\ -4 & -1 \end{bmatrix} \] **Task:** To find the matrix product \( BA \). ### Solution Steps: 1. **Matrix Dimensions:** Confirm that the matrices can be multiplied. Matrix \( B \) is a 2x2 matrix, and Matrix \( A \) is also a 2x2 matrix. Since the number of columns in \( B \) (2) is equal to the number of rows in \( A \) (2), the matrices can be multiplied. 2. **Multiplication Process:** Use the formula for matrix multiplication. For matrices \( B = [b_{ij}] \) and \( A = [a_{ij}] \), the element at \( (i, j) \) of the product \( BA \) is calculated as: \[ (BA)_{ij} = \sum_{k=1}^{n} b_{ik} \cdot a_{kj} \] **Calculation:** Let's denote: - \( B = \begin{bmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{bmatrix} = \begin{bmatrix} -2 & -3 \\ -4 & -1 \end{bmatrix} \) - \( A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} = \begin{bmatrix} -1 & -1 \\ -6 & -2 \end{bmatrix} \) The elements of the resulting matrix \( BA \) will be: - \( (BA)_{11} = (-2 \cdot -1) + (-3 \cdot -6) \) - \( (BA)_{12} = (-2 \cdot -1) + (-3 \cdot -2) \) - \( (BA)_{21} = (-4 \cdot -1) + (-1
Transcribed Image Text:### Matrix Multiplication: Finding BA **Objective:** Calculate the product of matrices B and A (denoted as BA). **Given Matrices:** Matrix \( A \): \[ A = \begin{bmatrix} -1 & -1 \\ -6 & -2 \end{bmatrix} \] Matrix \( B \): \[ B = \begin{bmatrix} -2 & -3 \\ -4 & -1 \end{bmatrix} \] **Task:** To find the matrix product \( BA \). ### Solution Steps: 1. **Matrix Dimensions:** Confirm that the matrices can be multiplied. Matrix \( B \) is a 2x2 matrix, and Matrix \( A \) is also a 2x2 matrix. Since the number of columns in \( B \) (2) is equal to the number of rows in \( A \) (2), the matrices can be multiplied. 2. **Multiplication Process:** Use the formula for matrix multiplication. For matrices \( B = [b_{ij}] \) and \( A = [a_{ij}] \), the element at \( (i, j) \) of the product \( BA \) is calculated as: \[ (BA)_{ij} = \sum_{k=1}^{n} b_{ik} \cdot a_{kj} \] **Calculation:** Let's denote: - \( B = \begin{bmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{bmatrix} = \begin{bmatrix} -2 & -3 \\ -4 & -1 \end{bmatrix} \) - \( A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} = \begin{bmatrix} -1 & -1 \\ -6 & -2 \end{bmatrix} \) The elements of the resulting matrix \( BA \) will be: - \( (BA)_{11} = (-2 \cdot -1) + (-3 \cdot -6) \) - \( (BA)_{12} = (-2 \cdot -1) + (-3 \cdot -2) \) - \( (BA)_{21} = (-4 \cdot -1) + (-1
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