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Chapter 9: Problem 69

Describe how to subtract matrices.

Short Answer

Expert verified
Matrices need to be the same size to subtract them. Subtract the corresponding entries of the matrices once they have been lined up. This is done entrywise.

Step by step solution

01

Check Matrix Sizes

First, confirm that the matrices to be subtracted are of the same size. This means they should have the same number of rows and the same number of columns. If they are not of the same size, you cannot subtract them.
02

Line up the Matrices

The second step is to line up the matrices. This helps ensure that the corresponding entries are clear and helps avoid mistakes during subtraction.
03

Perform the Subtraction

For the third step, subtract the corresponding entries in the matrices. This means you subtract the entry in the first row and first column of the first matrix from the entry in the first row and first column of the second matrix. This action is repeated for all entries.

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Most popular questions from this chapter

Describe matrices that cannot be added or subtracted.

Find the following matrices: a. \(A+B\) b. \(A-B\) c. \(-4 A\) d. \(3 A+2 B\) $$ A=\left[\begin{array}{r} {2} \\ {-4} \\ {1} \end{array}\right], \quad B=\left[\begin{array}{r} {-5} \\ {3} \\ {-1} \end{array}\right] $$

Find (if possible) the following matrices: a. \(A B\) b. \(B A\) $$ A=\left[\begin{array}{ll} {2} & {4} \\ {3} & {1} \\ {4} & {2} \end{array}\right], \quad B=\left[\begin{array}{rrr} {3} & {2} & {0} \\ {-1} & {-3} & {5} \end{array}\right] $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Matrix row operations remind me of what I did when solving a linear system by the addition method, although I no longer write the variables.

Find the following matrices: a. \(A+B\) b. \(A-B\) c. \(-4 A\) d. \(3 A+2 B\) $$ A=\left[\begin{array}{rrr} {2} & {-10} & {-2} \\ {14} & {12} & {10} \\ {4} & {-2} & {2} \end{array}\right], \quad B=\left[\begin{array}{rrr} {6} & {10} & {-2} \\ {0} & {-12} & {-4} \\ {-5} & {2} & {-2} \end{array}\right] $$
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