Evaluate the determinant of the matrix. Expand by minors along the row or column that appears to make the computation easiest.
$[1041−42−123]\left[ \begin{array} { c c c } 1 & 0 & 4 \\1 & - 4 & 2 \\- 1 & 2 & 3\end{array} \right]$

A) -5
B) 11
C) 8
D) -24
E) -4

Question

Evaluate the determinant of the matrix. Expand by minors along the row or column that appears to make the computation easiest.

[1041−42−123]\left[ \begin{array} { c c c } 1 & 0 & 4 \\1 & - 4 & 2 \\- 1 & 2 & 3\end{array} \right]

A) -5
B) 11
C) 8
D) -24
E) -4

Stefanny Aldana Vanegas · Accepted Answer

Final Answer : D, Explanation :   Expanding along the first column gives   − 1 [ 1 2 − 4 2 ] − 4 [ 1 4 − 1 3 ] + 0 [ 1 1 − 4 − 1 ] = − 1 ( − 8 ) − 4 ( 13 ) + 0 = − 24 . -1\begin{bmatrix} 1 & 2 \-4 & 2 \end{bmatrix} -4\begin{bmatrix}1 & 4 \ -1 & 3\end{bmatrix}+0\begin{bmatrix} 1 & 1\-4 & -1\end{bmatrix} = -1(-8)-4(13)+0 = \boxed{-24}. − 1 [ 1 − 4 ​ 2 2 ​ ] − 4 [ 1 − 1 ​ 4 3 ​ ] + 0 [ 1 − 4 ​ 1 − 1 ​ ] = − 1 ( − 8 ) − 4 ( 13 ) + 0 = − 24 ​ .

Evaluate the determinant of the matrix. Expand by minors along the row or column that appears to make the computation easiest.
$[1041−42−123]\left[ \begin{array} { c c c } 1 & 0 & 4 \\1 & - 4 & 2 \\- 1 & 2 & 3\end{array} \right]$

A) -5
B) 11
C) 8
D) -24
E) -4

Definitions

Learning Objectives

Learning Objectives

Related questions

Evaluate the determinant of the matrix. Expand by minors along the row or column that appears to make the computation easiest. [1041−42−123]\left[ \begin{array} { c c c } 1 & 0 & 4 \\1 & - 4 & 2 \\- 1 & 2 & 3\end{array} \right]​11−1​0−42​423​​ A) -5B) 11C) 8D) -24E) -4

Definitions

Learning Objectives

Learning Objectives

Related questions

Evaluate the determinant of the matrix. Expand by minors along the row or column that appears to make the computation easiest.
$[1041−42−123]\left[ \begin{array} { c c c } 1 & 0 & 4 \\1 & - 4 & 2 \\- 1 & 2 & 3\end{array} \right]$

A) -5
B) 11
C) 8
D) -24
E) -4