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Chapter 6: Problem 72

Describe how to multiply matrices.

Short Answer

Expert verified
Multiplying matrices involves creating a result matrix where each entry is obtained by multiplying every element in a row of the first matrix by the corresponding element in the column of the second matrix, summing up the results.

Step by step solution

01

Ensure correct matrix dimensions

Check the dimensions of the matrices to be multiplied. If a matrix A has dimensions 'm by n', and a matrix B has dimensions 'p by q', then 'n' (the number of columns in A) must equal 'p' (the number of rows in B) for the multiplication to be possible.
02

Initiate a result matrix

Create a result matrix with dimensions 'm by q' (this means it has the same number of rows as the first matrix and the same number of columns as the second one). This matrix will store the result of the multiplication.
03

Carry out the multiplication and addition step

For each entry in the result matrix, multiply every element in a row of the first matrix by the corresponding element in the column of the second matrix, adding up the results. The resultant value is the corresponding entry in the result matrix.
04

Fill the result matrix

Repeat step 3 for all rows of the first matrix and all columns of the second matrix to complete all entries in the result matrix.

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Most popular questions from this chapter

Exercises \(77-79\) will help you prepare for the material covered in the first section of the next chapter. Consider the equation \(\frac{x^{2}}{9}+\frac{y^{2}}{4}-1\) a. Set \(y-0\) and find the \(x\) -intercepts. b. Set \(x-0\) and find the \(y\) -intercepts.

Explain how to find the multiplicative inverse for a \(3 \times 3\) invertible matrix.

Describe how to perform scalar multiplication. Provide an example with your description.

Exercises \(77-79\) will help you prepare for the material covered in the first section of the next chapter. Divide both sides of \(25 x^{2}+16 y^{2}-400\) by 400 and simplify.

Use a graphing utility to find the multiplicative inverse of each matrix. Check that the displayed inverse is correct. $$\left[\begin{array}{llll}1 & 2 & 0 & 0 \\\0 & 0 & 1 & 0 \\\1 & 3 & 0 & 1 \\\4 & 0 & 0 & 2 \end{array}\right]$$
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