Problem 72
Question
Describe how to multiply matrices.
Step-by-Step Solution
Verified Answer
Matrix multiplication involves summing the product of corresponding entries from the rows of the first matrix with the columns of the second. The product is only defined if the number of columns in the first matrix equals the number of rows in the second, and the result will have the same number of rows as the first matrix and the same number of columns as the second.
1Step 1: Identification of matrix dimensions
Identify the dimensions of the two matrices to be multiplied. If the first matrix is of dimension m x n, and the second matrix is of dimension n x p, then the multiplication is possible. The resultant matrix will be of dimension m x p.
2Step 2: Setting up multiplication
Set up the multiplication. Begin with the first row of the first matrix and the first column of the second matrix. Multiply corresponding entries and then add them up.
3Step 3: Repeat for remaining elements
Repeat this process for the remaining rows of the first matrix and columns of the second matrix to fill out the rest of the entries in the resulting m x p matrix.
Other exercises in this chapter
Problem 71
a. Evaluate: \(\left|\begin{array}{ll}{a} & {a} \\ {0} & {a}\end{array}\right|\) b. Evaluate: \(\left|\begin{array}{ccc}{a} & {a} & {a} \\ {0} & {a} & {a} \\\ {
View solution Problem 71
Write each system in the form \(A X=B .\) Then solve the system by entering \(A\) and \(B\) into your graphing utility and computing \(A^{-1} B\) $$ \left\\{\be
View solution Problem 72
Exercises \(72-74\) will help you prepare for the material covered in the next section. In each exercise, refer to the following system: $$ \left\\{\begin{align
View solution Problem 72
$$ \text { Evaluate: }:\left(\begin{array}{lllll} {2} & {0} & {0} & {0} & {0} \\ {0} & {3} & {0} & {0} & {0} \\ {0} & {0} & {2} & {0} & {0} \\ {0} & {0} & {0} &
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