Question

question 38 points 2

consider \\(x = \

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

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

-5

20

Explanation:

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<reasoning>

Identify the given matrix and target operation

Using the Matrix Determinant knowledge point
\[
X =

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

\]
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

$$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$

= 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
\[
|X| = 20 - 25 = -5
\]
</reasoning>

<answer>
<mcq-correct>(A) -5</mcq-correct>
<mcq-option>(B) 20</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the given matrix and target operation

Using the Matrix Determinant knowledge point
\[
X =

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

\]
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

$$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$

= 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
\[
|X| = 20 - 25 = -5
\]
</reasoning>

<answer>
<mcq-correct>(A) -5</mcq-correct>
<mcq-option>(B) 20</mcq-option>
</answer>

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