Matrices and Determinants · Mathematics · KCET

$$\text { The value of }\left|\begin{array}{ccc} \sin ^2 14^{\circ} & \sin ^2 66^{\circ} & \tan 135^{\circ} \\ \sin ^2 66^{\circ} & \tan 135^{\circ} &...

If $$x\left[\begin{array}{l}3 \\ 2\end{array}\right]+y\left[\begin{array}{r}1 \\ -1\end{array}\right]=\left[\begin{array}{l}15 \\ 5\end{array}\right]$...

If $$A$$ and $$B$$ are two matrices, such that $$A B=B$$ and $$B A=A$$, then $$A^2+B^2$$ equals to

If $$A=\left[\begin{array}{cc}2-k & 2 \\ 1 & 3-k\end{array}\right]$$ is singular matrix, then the value of $$5 k-k^2$$ is equal to

If $$\Delta=\left|\begin{array}{ccc}1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2\end{array}\right|$$ and $$\Delta_1=\left|\begin{array}{ccc}1 & 1 & 1 \\ ...

If $$A=\left[\begin{array}{cc}1 & \tan \alpha / 2 \\ -\tan \alpha / 2 & 1\end{array}\right]$$ and $$A B=I$$, then $$B$$ is equal to

If $$A$$ is a matrix of order $$3 \times 3$$, then $$\left(A^2\right)^{-1}$$ is equal to

If $$A=\left[\begin{array}{ll}2 & -1 \\ 3 & -2\end{array}\right]$$, then the inverse of the matrix $$A^3$$ is

If $$A$$ is a skew symmetric matrix, then A$$^{2021}$$ is

If $$A=\left[\begin{array}{ll}0 & 1 \\ 0 & 0\end{array}\right]$$, then $$(a I+b A)^n$$ is (where $$I$$ is the identify matrix of order 2)

If $$A$$ is a $$3 \times 3$$ matrix such that $$|5 \cdot \operatorname{adj} A|=5$$, then $$|A|$$ is equal to

If there are two values of '$$a$$' which makes determinant $$\Delta=\left|\begin{array}{ccc} 1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2 a \end{array}\right...

If $$A_n=\left[\begin{array}{cc}1-n & n \\ n & 1-n\end{array}\right]$$, then $$\left|A_1\right|+\left|A_2\right|+\ldots .\left|A_{2021}\right|=$$...

If $$A=\left[\begin{array}{ccc}1 & -2 & 1 \\ 2 & 1 & 3\end{array}\right]$$ $$ B=\left[\begin{array}{ll}2 & 1 \\ 3 & 2 \\ 1 & 1\end{array}\right]$$, th...

Let $$M$$ be $$2 \times 2$$ symmetric matrix with integer entries, then $$M$$ is invertible if

If $$A$$ and $$B$$ are matrices of order 3 and $$|A|=5,|B|=3$$, then $$|3 A B|$$ is

If $$A$$ and $$B$$ are invertible matrices then which of the following is not correct?

If $$x^3-2 x^2-9 x+18=0$$ and $$A=\left|\begin{array}{lll}1 & 2 & 3 \\ 4 & x & 6 \\ 7 & 8 & 9\end{array}\right|$$ then the maximum value of $$A$$ is...