How do you multiply matrices given #A=((0, 2, 1), (-5, -1, 0))# and #B=((1, -4), (0, 1), (5, -1))#?

Question

Elijah Allen · Accepted Answer

The answer is #=((5,1),(-5,19))#

If you possess the ability to multiply two matrices

#((a,b,c),(d,e,f))*((k,l),(m,n),(p,q))#

#=((ak+bm+cp,al+bn+cq),(dk+em+fp,dl+en+fq))#

Consequently,

#((0,2,1),(-5,-1,0))*((1,-4),(0,1),(5,-1))#

#=((5,1),(-5,19))#

Serenity Jones · Answer

undefined To multiply matrices A and B, the number of columns in matrix A must be equal to the number of rows in matrix B. In this case, A is a 2x3 matrix and B is a 3x2 matrix, so multiplication is possible.

The resulting matrix will have dimensions equal to the number of rows in matrix A and the number of columns in matrix B, which is a 2x2 matrix.

To calculate the elements of the resulting matrix, each element in the resulting matrix is obtained by taking the dot product of the corresponding row of matrix A and the corresponding column of matrix B.

Let's denote the resulting matrix as C.

$$C_{ij} = \sum_{k=1}^{3} A_{ik} \cdot B_{kj}$$

$$C_{11} = (0 \cdot 1) + (2 \cdot 0) + (1 \cdot 5) = 5$$

$$C_{12} = (0 \cdot (-4)) + (2 \cdot 1) + (1 \cdot (-1)) = 1$$

$$C_{21} = (-5 \cdot 1) + (-1 \cdot 0) + (0 \cdot 5) = -5$$

$$C_{22} = (-5 \cdot (-4)) + (-1 \cdot 1) + (0 \cdot (-1)) = 19$$

Therefore, the resulting matrix C is:

$$C = \begin{pmatrix} 5 & 1 \ -5 & 19 \end{pmatrix}$$