Determinants and their Applications — Practice Quiz
Telangana Open School (TOSS) · Class 12 · Mathematics
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Quick Quiz: Determinants and their Applications
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What is the value of the determinant $\begin{vmatrix} 2 & 3 \\ 4 & 5 \end{vmatrix}$?
If $\begin{vmatrix} x & 2 \\ 3 & 4 \end{vmatrix} = 2$, what is the value of $x$?
The determinant $\begin{vmatrix} a & b \\ c & d \end{vmatrix}$ is equal to:
What is the determinant of $\begin{vmatrix} 5 & 0 \\ 0 & 5 \end{vmatrix}$?
Sample Questions
If the determinant of a 2×2 matrix is zero, the matrix is called:
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Singular matrix
A square matrix with determinant zero is called a singular matrix.
The value of $\begin{vmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{vmatrix}$ is:
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1
$\cos \theta \cdot \cos \theta - (-\sin \theta) \cdot \sin \theta = \cos^2 \theta + \sin^2 \theta = 1$.
What is the minor of element $a_{22}$ in the determinant $\begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix}$?
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1
The minor of $a_{22}$ is the determinant obtained by deleting row 2 and column 2, which leaves the element 1.
The cofactor of an element $a_{ij}$ is given by:
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(-1)^{i+j} × minor
The cofactor is $(-1)^{i+j}$ times the minor of the element.
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