Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Dec 01, 2023

Find the value of the $3 \times 3$ determinant: $\left|\begin{array}{ccc} 3 & -3 & 0 \\ 1 & -2 & 1 \\ -2 & 1 & 2 \end{array}\right|$

STEP 1

Assumptions
1. We are given a 3x3 matrix and we need to find its determinant.
2. The matrix is $\left|\begin{array}{ccc} 3 & -3 & 0 \\ 1 & -2 & 1 \\ -2 & 1 & 2 \end{array}\right|$

STEP 2

The determinant of a 3x3 matrix can be found using the formula:
$\begin{vmatrix}a & b & c\\d & e & f\\g & h & i\end{vmatrix} = aei + bfg + cdh - ceg - bdi - afh$

STEP 3

Now, plug in the given values from the matrix into the formula.
$\begin{vmatrix}3 & -3 & 0\\1 & -2 & 1\\-2 & 1 & 2\end{vmatrix} = 3(-2)2 + (-3)12 + 011 - 0(-2)2 - (-3)12 - 311$

STEP 4

Simplify the expression.
$= -12 -6 + 0 - 0 + 6 - 3$

STEP 5

Calculate the determinant.
$= -12 - 3 = -15$
The value of the determinant is -15.

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