Math

QuestionMultiply matrices AA and BB and find the value of cell C12\mathrm{C}_{12} in the product matrix CC.

Studdy Solution

STEP 1

Assumptions1. Matrix A is a1x3 matrix. Matrix B is a3x3 matrix3. We are asked to find the element in the first row and second column of the product of A and B, denoted as C_{12}

STEP 2

First, let's recall how to multiply matrices. The element in the i-th row and j-th column of the product of two matrices is obtained by multiplying each element in the i-th row of the first matrix by the corresponding element in the j-th column of the second matrix, and then summing these products.

STEP 3

To find C_{12}, we need to multiply each element in the first row of matrix A by the corresponding element in the second column of matrix B, and then sum these products.

STEP 4

Write down the elements in the first row of matrix A and the second column of matrix B.
A1=[3,8,6]A_{1*} = [3,8,6]B2=[8,,2]B_{*2} = [8,,2]

STEP 5

Now we multiply each element in A_{1*} by the corresponding element in B_{*2} and sum these products to find C_{12}.
C12=A11B12+A12B22+A13B32C_{12} = A_{11} \cdot B_{12} + A_{12} \cdot B_{22} + A_{13} \cdot B_{32}

STEP 6

Substitute the values for A_{11}, A_{12}, A_{13}, B_{12}, B_{22}, and B_{32} into the equation.
C12=38+85+62C_{12} =3 \cdot8 +8 \cdot5 +6 \cdot2

STEP 7

Calculate the value of C_{12}.
C12=3+5+62=24+40+12=76C_{12} =3 \cdot + \cdot5 +6 \cdot2 =24 +40 +12 =76The element in the first row and second column of the product of matrices A and B, denoted as C_{12}, is76.

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