Determinants Te...

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

If x, y, z are all different from zero and \(\begin{vmatrix} 1 + x&1 & 1 \\[0.3em] 1& 1+y &1 \\[0.3em] 1 & 1& 1+z \end{vmatrix}\) = 0, then value of \(x ^{–1} + y ^{–1} + z ^{–1}\) is

The value of the determinant \(\begin{vmatrix} x& x+y& x + 2y \\[0.3em] x + 2y& x & x+y \\[0.3em] x+y & x+2y &x \end{vmatrix}\) is

There are two values of a which makes determinant, \(\Delta = \) \(\begin{vmatrix} 1 & -2& 5 \\[0.3em] 2 & a &-1 \\[0.3em] 0 &4&2a \end{vmatrix}\) = 86, then sum of these number is

If A = \(\begin{bmatrix} -1& \frac{3}{2} \\[0.3em] \frac{-1}{2} & \frac{1}{2} \\[0.3em] \end{bmatrix}\), then \(A^3\)

If A = \(\begin{bmatrix} 2& 1 \\[0.3em] -4 & -2\\[0.3em] \end{bmatrix}\), then the value of I + 2A + 3\(A^2\) + .......... \(\infty\) is

If A = \(\begin{bmatrix} -2& 3 \\[0.3em] -1& 1 \\[0.3em] \end{bmatrix}\), then I + A + \(A^2\) + ..... \(\infty\) = ......

If A = \(\begin{bmatrix} 3& 1 \\[0.3em] -9 & -3 \\[0.3em] \end{bmatrix}\), then I + 2A + 3\(A^2\) + .....\(\infty\) = ....

If the value of determinant \(\begin{vmatrix} a &1 & 1 \\[0.3em] 1 & b & 1\\[0.3em] 1 & 1 & c \end{vmatrix}\) is positive, then

If a, b, c are positive and not all equal, then the value of determinant \(\begin{vmatrix} a& b & c \\[0.3em] b& c & a \\[0.3em] c & a& b \end{vmatrix}\)