Ch. 6 - Matrices and Determinants

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Blitzer 8th Edition

Ch. 6 - Matrices and Determinants

Problema 9b

Capitolo 7, Problema 9b

In Exercises 9 - 16, find the following matrices: b. A - B

Guida verificata passo dopo passo

Step 1: Understand the problem. You are asked to find the matrix A - B, where matrices A and B are given as:

A= [\begin{matrix} 4 & 1 \\ 3 & 2 \end{matrix}]

and

B= [\begin{matrix} 5 & 9 \\ 0 & 7 \end{matrix}]

Step 2: Recall the rule for matrix subtraction. To subtract two matrices, subtract their corresponding elements. That is, if

A = [a_{ij}]

and

B = [b_{ij}]

, then

A - B = [a_{ij} - b_{ij}]

Step 3: Set up the subtraction element-wise. For each element in the resulting matrix, subtract the element in B from the corresponding element in A:

A - B = \(\begin{bmatrix}\) 4 - 5 & 1 - 9 \\ 3 - 0 & 2 - 7 \(\end{bmatrix}\)

Step 4: Write the resulting matrix with the subtracted elements (do not calculate the final values yet). This matrix represents the difference between A and B.

Step 5: Verify that both matrices A and B have the same dimensions (2x2), which is necessary for subtraction to be valid.

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Matrix subtraction involves subtracting corresponding elements of two matrices of the same dimensions. Each element in the resulting matrix is found by subtracting the element in matrix B from the element in matrix A at the same position.

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Pratica correlata

Domanda del libro di testo

In Exercises 8–11, use Gaussian elimination to find the complete solution to each system, or show that none exists.

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Domanda del libro di testo

In Exercises 9 - 16, find the following matrices: c. - 4A

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