Question

question 38 points 2

consider \\(x = \

$$\begin{bmatrix} 10 & 5 \\\\ 5 & 2 \\end{bmatrix}$$

\\). find \\(|x|\\).

-5

20

Explanation:

Identify the given matrix and target operation

Using the Matrix Determinant knowledge point

$$ X =
LATEXBLOCK0
$$

We need to find \(|X|\), which represents the determinant of the \(2 \times 2\) matrix \(X\).

Apply the determinant formula

Using the Matrix Determinant knowledge point

$$ |X| = \det
LATEXBLOCK1
= ad - bc $$

Substituting the values \(a = 10\), \(b = 5\), \(c = 5\), and \(d = 2\):

$$ |X| = (10)(2) - (5)(5) $$

Calculate the final value

Using the Matrix Determinant knowledge point

$$ |X| = 20 - 25 = -5 $$

Answer:

• (A) -5 (Correct answer)
• (B) 20