Guided Example #2 - Matrices - Determinants and Cramer's Rule

Consider ${\begin{cases} 3 x - y + z = 5 \\ x + 2 y - 2 z = - 3 \\ 2 x + 3 y + z = 4 \end{cases}$

If the above system is solved by using Cramer's Rule, the numerator determinant for $y (D_{y})$ is

a. 28
b. 0
c. 56
d. None of the above

The correct answer is B. To see why, view each of the steps below.

Step 1

Using the determinants, $y = \frac{D_{y}}{D}$ , where $D_{y} = | \begin{matrix} 3 & 5 & 1 \\ 1 & - 3 & - 2 \\ 2 & 4 & 1 \end{matrix} | = 3 | \begin{matrix} - 3 & - 2 \\ 4 & 1 \end{matrix} | - 5 | \begin{matrix} 1 & - 2 \\ 2 & 1 \end{matrix} | - 1 | \begin{matrix} 1 & - 3 \\ 2 & 4 \end{matrix} | = 3 (- 3 - (- 8)) - 5 (1 - (- 4)) - 1 (4 - (- 6)) = 3 (5) - 5 (5) - 10 = 15 - 25 - 10 = 0.$

Guided Example #2 - Matrices - Determinants and Cramer's Rule

Step 1

All Steps