Calculate the values based on the given equations from the matrices.

Understand the Problem

The question involves calculating the determinants or some computations related to matrices. It outlines equations involving matrix elements and aims to reach a final value through arithmetic operations.

Answer

First row: $-11$, Second row: $-16$, Third row: $30$

Steps to Solve

Calculate the first row of the matrix For the first row, we have the expression: $(-3 \cdot 3) + (0 \cdot 2) + (-2 \cdot 1)$ Calculating this: $$-9 + 0 - 2 = -11$$
Calculate the second row of the matrix For the second row, the expression is: $(-5 \cdot 3) + (0 \cdot 2) + (-1 \cdot 1)$ Calculating this: $$-15 + 0 - 1 = -16$$
Calculate the third row of the matrix For the third row, we have: $(-2 \cdot 3) + (13 \cdot 2) + (10 \cdot 1)$ Calculating this: $$-6 + 26 + 10 = 30$$
Summarize the results The computed values for the rows are:

First row: $-11$
Second row: $-16$
Third row: $30$

The results of the matrix computations are:

First row: $-11$
Second row: $-16$
Third row: $30$

More Information

These calculations involve basic operations of multiplication and addition, which are fundamental in linear algebra. Each row corresponds to a linear combination of the variables represented by matrix elements.

Tips

Incorrect multiplication: Make sure to multiply the coefficients with their corresponding values accurately.
Sign errors: Pay careful attention to positive and negative signs during calculations to avoid mistakes.

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