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Ch. 6 - Matrices and Determinants
Blitzer - College Algebra 8th Edition
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Tutti i libri di testoBlitzer 8th EditionCh. 6 - Matrices and DeterminantsProblema 43
Capitolo 7, Problema 43

In Exercises 37 - 44, perform the indicated matrix operations given that A, B and C are defined as follows. If an operation is not defined, state the reason.
A=[40−3501],B=[51−2−2],C=[1−1−11]A=\(\begin{bmatrix}\)4 & 0\\ -3 & 5\\ 0 & 1\(\end{bmatrix}\),B=\(\begin{bmatrix}\)5 & 1\\ -2 & -2\(\end{bmatrix}\),C=\(\begin{bmatrix}\)1 & -1\\ -1 & 1\(\end{bmatrix}\)
A(BC)

Guida verificata passo dopo passo
1
Step 1: Identify the matrices A, B, and C as given: \(A = \begin{bmatrix} 4 & 0 \\ -3 & 5 \\ 0 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} 5 & 1 \\ -2 & -2 \end{bmatrix}, \quad C = \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix}\)
Step 2: Determine the dimensions of each matrix to check if the operations are defined: - Matrix A is 3x2 (3 rows, 2 columns) - Matrix B is 2x2 - Matrix C is 2x2
Step 3: Compute the product BC first since the expression is A(BC). Since B is 2x2 and C is 2x2, the product BC is defined and will result in a 2x2 matrix. Use matrix multiplication rules: \( (BC)_{ij} = \sum_{k=1}^{2} B_{ik} \times C_{kj} \)
Step 4: After finding BC (a 2x2 matrix), multiply A (3x2) by BC (2x2). Since the number of columns in A (2) matches the number of rows in BC (2), the product A(BC) is defined and will result in a 3x2 matrix. Use matrix multiplication rules again: \( (A(BC))_{ij} = \sum_{k=1}^{2} A_{ik} \times (BC)_{kj} \)
Step 5: Perform the multiplications and additions step-by-step for each element of the resulting matrix to find A(BC). Remember to multiply corresponding elements and sum them for each position in the product matrix.

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Perform the indicated matrix operations given that A, B and C are defined as follows. If an operation is not defined, state the reason.

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