Mathematics Tes...

A square matrix is called singular if _________.

If A is a singular matrix, then A(adj A) is a / an

If \(\rm A=\begin{bmatrix} 1& 3\\ 5& 2\end{bmatrix}\) and \(\rm B=\begin{bmatrix} 3&2\\ 1& 3\end{bmatrix}\), then |AB| = ?

If A is an orthogonal matrix, then |A| is

The equations 2x - ky + 7 = 0 and 6x - 12y + 15 = 0 have no solution for

The area of triangle with vertices (K, 0), (4, 0), (0, 2) is 4 square units, then value of K is

Find the value of a, b, c and d if: \(\left[ {\begin{array}{*{20}{c}} {a - b}&{2a + c}\\ {2a - b}&{3c + d} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 1}&5\\ 0&{13} \end{array}} \right]\)

The system of linear equation kx + y + z = 1, x + ky + z = 1 and x + y + kz = 1 has a unique solution under which one of the following conditions?

If x y z are all different and not equal to zero and \(\left| {\begin{array}{*{20}{c}} {1 + x}&1&1\\ 1&{1 + y}&1\\ 1&1&{1 + z} \end{array}} \right| = 0\) then the value of x^-1 + y^-1 + z^-1 is equal to

What is the minor, M₂₃ of \( \begin{bmatrix} 0 & 4 & 6\\ -4 & 0&-2 \\ -6& 2 & 0 \end{bmatrix}\)