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Chapter 6: Problem 69

Describe how to subtract matrices.

Short Answer

Expert verified
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 by step solution

01

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 \(B = \begin{bmatrix} b_{11} & b_{12} \ b_{21} & b_{22} \end{bmatrix}\)
02

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 \(a_{22} - b_{22}\)
03

Create the Result Matrix

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

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Most popular questions from this chapter

Let $$\begin{aligned}&A=\left[\begin{array}{ll}1 & 0 \\\0 & 1\end{array}\right], \quad B=\left[\begin{array}{rr}1 & 0 \\\0 & -1\end{array}\right], \quad C=\left[\begin{array}{rr}-1 & 0 \\ 0 & 1\end{array}\right]\\\&D=\left[\begin{array}{rr}-1 & 0 \\\0 & -1\end{array}\right]\end{aligned}$$ Use any three of the matrices to verify a distributive property.

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