QuestionWhat is the value of $A B_{22}$ given the matrix multiplication result $A B = \left[\begin{array}{cc} 18 & 45 \\ 25 & 40 \end{array}\right]$ ?

Studdy Solution

STEP 1

Assumptions1. Matrix multiplication is performed row by column. . The result of the multiplication of two matrices is another matrix.
3. The element in the i-th row and j-th column of the resulting matrix is obtained by multiplying the elements of the i-th row of the first matrix by the elements of the j-th column of the second matrix and adding them up.
4. The subscript notation $B_{22}$ refers to the element in the second row and second column of matrix $B$ .
5. The notation $AB_{22}$ refers to the element in the second row and second column of the resulting matrix $AB$ .

STEP 2

First, we need to identify the element $B_{22}$ in matrix $B$ . This is the element in the second row and second column.
$B_{22} =2$

STEP 3

Next, we need to identify the element $AB_{22}$ in the resulting matrix $AB$ . This is the element in the second row and second column.
$AB_{22} =40$

STEP 4

Finally, we calculate the value of the result $AB_{22}$ .
$AB_{22} =40$ The value of the result $AB_{22}$ is40.

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