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Find the values of $x$ if $\begin{vmatrix}3 & 1 & x \\-1 & 3 & 4 \\ x & 1 & 0 \end{vmatrix}=-30$

NETNUST Entry TestMathematicsMatrices and Determinants

If determinant of $A=\begin{bmatrix}4& 0 &0 \\0&-2& 0 \\0&0&3 \end{bmatrix}$ then $A_{11}$=

NETNUST Entry TestMathematicsMatrices and Determinants

The value of determinant of $\begin{bmatrix}1& a &b+c \\1&b& c+a \\1&c&a+b \end{bmatrix}$ is

NETNUST Entry TestMathematicsMatrices and Determinants

Determinant of $\begin{bmatrix}x& 1& 1 &1 \\1&x & 1 & 1\\1&1&x & 1\\1&1&1&x \end{bmatrix}$=

NETNUST Entry TestMathematicsMatrices and Determinants

Determinant of $\begin{bmatrix}rcos\theta& 1&-sin\theta\\0&1 & 0\\rsin\theta&0&cos\theta \end{bmatrix}$=

NETNUST Entry TestMathematicsMatrices and Determinants

Determinant of $\begin{bmatrix}1& 1&1\\1&1+x & 1\\1&1&1+y\end{bmatrix}$=

NETNUST Entry TestMathematicsMatrices and Determinants

Determinant of $\begin{bmatrix}b+c& a&a\\b&c+a & b\\c&c&a+b\end{bmatrix}$=

NETNUST Entry TestMathematicsMatrices and Determinants

Determinant of $\begin{bmatrix}1^{2}& 2^{2}&3^{2}\\2^{2}&3^{2} & 4^{2}\\3^{2}&4^{2}&5^{2}\end{bmatrix}$=

NETNUST Entry TestMathematicsMatrices and Determinants

Determinant of $\begin{bmatrix}2a& 2b&2c\\a+b & 2b & b+c\\a+c&b+c&2c \end{bmatrix}$=

NETNUST Entry TestMathematicsMatrices and Determinants

Determinant of $\begin{bmatrix}\alpha& \beta+\gamma& 1 \\\beta & \gamma+\alpha & 1\\\gamma&\alpha+\beta&1 \end{bmatrix}$

NETNUST Entry TestMathematicsMatrices and Determinants

$\begin{bmatrix}b+c & a& a^{2} \\a+a & b & b^{2}\\a+b&c&c^{2} \end{bmatrix}$=

NETNUST Entry TestMathematicsMatrices and Determinants

$\begin{bmatrix}1 & 1& 1 \\a & b & c\\a^{2}&b^{2}&c^{2} \end{bmatrix}$=

NETNUST Entry TestMathematicsMatrices and Determinants

If a square matrix has two identical rows or two identical columns, then |A|=

NETNUST Entry TestMathematicsMatrices and Determinants

If in a square matrix A, two rows or two columns are interchanged the determinant of resulting matrix is

NETNUST Entry TestMathematicsMatrices and Determinants

If $A=\begin{bmatrix}1 & -2 & 3 \\-2 & 3 & 1 \\4 & -3& 2\end{bmatrix}$ then co factor $A_{32}$=

NETNUST Entry TestMathematicsMatrices and Determinants

The determinant of a $1\times 1$ matrix $\begin{bmatrix}a_{11} \end{bmatrix}$ is

NETNUST Entry TestMathematicsMatrices and Determinants

If $A=\begin{bmatrix}1 &0 \\0& 1 \end{bmatrix}$ then $A^{-1}$ is

NETNUST Entry TestMathematicsMatrices and Determinants

If A, B and C are three matrices, and A is non-singular then AB=AC if B=

NETNUST Entry TestMathematicsMatrices and Determinants

If $A=\begin{bmatrix}5 &-3 \\-4& 3 \end{bmatrix}$ then $A^{-1}$=

NETNUST Entry TestMathematicsMatrices and Determinants

Adjoint of matrix A is denoted by

NETNUST Entry TestMathematicsMatrices and Determinants

Which type of the matrix has no inverse?

NETNUST Entry TestMathematicsMatrices and Determinants

Let $A=\begin{bmatrix}2 &3 \\2& 2 \end{bmatrix}$ and $B=\begin{bmatrix}-1 &\frac{3}{2} \\1& -1 \end{bmatrix}$ if AB=BA then

NETNUST Entry TestMathematicsMatrices and Determinants

If $A=\begin{bmatrix}\iota & 0 \\1 & -\iota \end{bmatrix}$ then $A^{2}$=

NETNUST Entry TestMathematicsMatrices and Determinants

If $A=\begin{bmatrix}5 & 3 \\1 & 1 \end{bmatrix}$, then $A^{-1}$=

NETNUST Entry TestMathematicsMatrices and Determinants

The multiplicative inverse of matrix $A{A^{-1})$ is

NETNUST Entry TestMathematicsMatrices and Determinants