The Determinant

Practice Questions

Linear Algebra › The Determinant

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1

Calculate the determinant of matrix A.

$A =\begin{bmatrix} 5&3 \ 6&4 \end{bmatrix}$

2

Consider the matrix

$A = \begin{bmatrix} -1&4 &1 \ -2& 3& 1\ 1&6 & 2 \end{bmatrix}$ .

Give cofactor $C_{33}$ of this matrix.

3

Let be a four-by-four matrix.

Cofactor $C_{13}$ must be equal to:

4

Consider the matrix

$A = \begin{bmatrix} -1&4 &1 \ -2& 3& 1\ 1&6 & 2 \end{bmatrix}$ .

Give cofactor $C_{2 3}$ of this matrix.

5

Let be a five-by-five matrix.

Cofactor $C_{14}$ must be equal to:

6

Consider the matrix

$A = \begin{bmatrix} 2& 3& -1\ -2& 1& 0\ 0& 1& 2 \end{bmatrix}$

Calculate the cofactor $C_{2,1}$ of this matrix.

7

Calculate the determinant of matrix A.

$A=\begin{bmatrix} 2&5 &4 &7 &1 \ 8& 6&11 & 3&9 \4 & 1&3 &0 &6 \ 7& 0&2 &9 &1 \end{bmatrix}$

8

True or false: Square matrix is nilpotent if and only if $\det A = 0$ .

9

Calculate the determinant of $\begin{bmatrix} 5&-2 \ 1&3 \end{bmatrix}$ .

10

$A = \begin{bmatrix} 3&1 &0 \ 0&a &12 \ 1& 0 & a \end{bmatrix}$

is a singular matrix for what values of ?

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