Question

question 40 points 2

\\(\

$$\begin{bmatrix} 1 & 2 & 3 \\\\ 4 & 2 & 6 \\\\ 3 & 4 & 1 \\end{bmatrix}$$

\\). check whether the matrix a has an inverse.

no
yes

Explanation:

State the condition for matrix invertibility

Using the Matrix Inverse Existence knowledge point

$$ \text{A square matrix } A \text{ has an inverse if and only if } \det(A) e 0. $$

Define the matrix and set up the determinant

Using the Matrix Determinant knowledge point

$$ A =
LATEXBLOCK0
$$

$$ \det(A) =
LATEXBLOCK1
$$

Calculate the determinant using cofactor expansion

Using the Determinant Expansion knowledge point

$$
LATEXBLOCK2
$$

Determine if the inverse exists

Using the Matrix Inverse Existence knowledge point

$$ \det(A) = 36 e 0 \implies A \text{ has an inverse.} $$

Answer:

• No
• Yes (Correct answer)