Problem 69 - College Algebra

Question

Describe how to subtract matrices.

Step-by-Step Solution

Answer

The operation of matrix subtraction, \(A - B\), operates element-wise over the matrices, i.e., each element of Matrix B is subtracted from the corresponding element of Matrix A, producing a new matrix. The matrices need to be of the same dimensions for the operation to be valid.

Step 1: Assign the Matrix

Let's say the two matrices to be subtracted are \(A = \begin{bmatrix} a_{11} & a_{12} \ a_{21} & a_{22} \end{bmatrix}\) and \(B = \begin{bmatrix} b_{11} & b_{12} \ b_{21} & b_{22} \end{bmatrix}\)

Step 2: Subtract corresponding elements

Subtract corresponding elements of Matrix B from Matrix A, i.e., \(a_{11} - b_{11}\), \(a_{12} - b_{12}\), \(a_{21} - b_{21}\), and \(a_{22} - b_{22}\)

Step 3: Create the Result Matrix

The result is a new matrix, say Matrix C, which is given by \(C = A - B = \begin{bmatrix} a_{11} - b_{11} & a_{12} - b_{12} \ a_{21} - b_{21} & a_{22} - b_{22} \end{bmatrix}\)