Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Nov 21, 2023

Compute the product of the given $3 \times 1$ and $1 \times 3$ matrices.

STEP 1

Assumptions1. We are given two matrices, a1x3 matrix and a3x1 matrix. . We are asked to find the product of these two matrices.

STEP 2

The product of two matrices is found by multiplying corresponding entries and then summing those products. In this case, since we have a1x matrix and ax1 matrix, the result will be a1x1 matrix (a scalar).
The formula for the product of two matrices A and B is given by $C_{ij} = \sum_{k=1}^{n} A_{ik}B_{kj}$ where C is the resulting matrix, A and B are the matrices being multiplied, and n is the number of columns in A (or equivalently, the number of rows in B).

STEP 3

In our case, we only have one row and one column, so the formula simplifies to $C = \sum_{k=1}^{3} A_{1k}B_{k1}$

STEP 4

Now, let's plug in the values from our matrices into the formula $C = (-1)* +77 +1$

STEP 5

Calculate the result $C = -5 +49 +5$

STEP 6

implify the result $C =49$ So, the product of the given matrices is49.

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