MCQ (Single Correct Answer)
The values of x for which the given matrix $$\left[ {\matrix{
{ - x} & x & 2 \cr
2 & x & { - x} \cr
x & { - 2} & { - x} \cr
} } \righ...
If the matrix $$\left[ {\matrix{
a & b \cr
c & d \cr
} } \right]$$ is commutative with the matrix $$\left[ {\matrix{
1 & 1 \cr
0 &...
If A is a square matrix. Then
If A2 $$-$$ A + I = 0, then the inverse of the matrix A is
If A and B are square matrices of the same order and AB = 3I, then A$$-$$1 is equal to
If the matrices $$A = \left[ {\matrix{
2 & 1 & 3 \cr
4 & 1 & 0 \cr
} } \right]$$ and $$B = \left[ {\matrix{
1 & { - 1} \cr
0 & 2 ...
If $$\omega$$ is an imaginary cube root of unity and $$\left| {\matrix{
{x + {\omega ^2}} & \omega & 1 \cr
\omega & {{\omega ^2}} & {1 + x} ...
If $$A = \left[ {\matrix{
1 & 2 \cr
{ - 4} & { - 1} \cr
} } \right]$$ then A$$-$$1 is
If A and B are two matrices such that A + B and AB are both defined, then
If $$A = \left( {\matrix{
3 & {x - 1} \cr
{2x + 3} & {x + 2} \cr
} } \right)$$ is a symmetric matrix, then the value of x is
If $$z = \left| {\matrix{
1 & {1 + 2i} & { - 5i} \cr
{1 - 2i} & { - 3} & {5 + 3i} \cr
{5i} & {5 - 3i} & 7 \cr
} } \right|$$, then $$(...
If one of the cube roots of 1 be $$\omega$$, then $$\left| {\matrix{
1 & {1 + {\omega ^2}} & {{\omega ^2}} \cr
{1 - i} & { - 1} & {{\omega ^2}...
$$\left| {\matrix{
{a - b} & {b - c} & {c - a} \cr
{b - c} & {c - a} & {a - b} \cr
{c - a} & {a - b} & {b - c} \cr
} } \right| = $$...
Under which of the following condition(s) does(do) the system of equations $$\left( {\matrix{
1 & 2 & 4 \cr
2 & 1 & 2 \cr
1 & 2 & {(a - 4...
If $$\Delta (x) = \left| {\matrix{
{x - 2} & {{{(x - 1)}^2}} & {{x^3}} \cr
{x - 1} & {{x^2}} & {{{(x + 1)}^3}} \cr
x & {{{(x + 1)}^2}} & ...
If $$p = \left[ {\matrix{
1 & \alpha & 3 \cr
1 & 3 & 3 \cr
2 & 4 & 4 \cr
} } \right]$$ is the adjoint of the $$3 \times 3$$ matrix A...
If $$A = \left( {\matrix{
1 & 1 \cr
0 & i \cr
} } \right)$$ and $${A^{2018}} = \left( {\matrix{
a & b \cr
c & d \cr
} } \right...
The solution of $$\det (A - \lambda {I_2}) = 0$$ be 4 and 8 and $$A = \left( {\matrix{
2 & 2 \cr
x & y \cr
} } \right)$$. Then
(I2 is iden...
If M is a 3 $$\times$$ 3 matrix such that (0, 1, 2) M = (1 0 0), (3, 4 5) M = (0, 1, 0), then (6 7 8) M is equal to
Let $$A = \left( {\matrix{
1 & 0 & 0 \cr
0 & {\cos t} & {\sin t} \cr
0 & { - \sin t} & {\cos t} \cr
} } \right)$$Let $$\lambda$$1, $$...
Let A and B two non singular skew symmetric matrices such that AB = BA, then A2B2(ATB)$$-$$1(AB$$-$$1)T is equal to ...
If an (> 0) be the nth term of a G.P. then$$\left| {\matrix{
{\log {a_n}} & {\log {a_{n + 1}}} & {\log {a_{n + 2}}} \cr
{\log {a_{n + 3}}} & {...
Let T and U be the set of all orthogonal matrices of order 3 over R and the set of all non-singular matrices of order 3 over R respectively. Let A = {...
The determinant $$\left| {\matrix{
{{a^2} + 10} & {ab} & {ac} \cr
{ab} & {{b^2} + 10} & {bc} \cr
{ac} & {bc} & {{c^2} + 10} \cr
} } \...
Let A = $$\left( {\matrix{
{3 - t} \cr
{ - 1} \cr
0 \cr
} \matrix{
{} \cr
{} \cr
{} \cr
} \,\matrix{
1 \cr
{...
Let $$A = \left[ {\matrix{
{12} & {24} & 5 \cr
x & 6 & 2 \cr
{ - 1} & { - 2} & 3 \cr
} } \right]$$. The value...
Let $$A = \left( {\matrix{
a & b \cr
c & d \cr
} } \right)$$ be a 2 $$ \times $$ 2 real matrix with det A = 1. If the equation det...
If $$\left| {\matrix{
{{a^2}} & {bc} & {{c^2} + ac} \cr
{{a^2} + ab} & {{b^2}} & {ca} \cr
{ab} & {{b^2} + bc} & {...
If f : S $$ \to $$ R, where S is the set of all non-singular matrices of order 2 over R and $$f\left[ {\left( {\matrix{
a & b \cr
c & ...
If the vectors $$\alpha = \widehat i + a\widehat j + {a^2}\widehat k,\,\beta = \widehat i + b\widehat j + {b^2}\widehat k$$ and $$\,\gamma = \wideh...
Let A be a square matrix of order 3 whose all entries are 1 and let I3 be the identity matrix of order 3. Then, the matrix $$A - 3{I_3}$$ is ...
If M is any square matrix of order 3 over R and if M' be the transpose of M, then adj(M') $$-$$ (adj M)' is equal to
If $$A = \left( {\matrix{
5 & {5x} & x \cr
0 & x & {5x} \cr
0 & 0 & 5 \cr
} } \right)$$ and $$|A{|^2} = 25$$,...
Let A and B be two square matrices of order 3 and AB = O3, where O3 denotes the null matrix of order 3. Then,
The system of equations$$\eqalign{
& \lambda x + y + 3z = 0 \cr
& 2x + \mu y - z = 0 \cr
& 5x + 7y + z = 0 \cr} $$has infinitely...
If $$\left| {\matrix{
{ - 1} & 7 & 0 \cr
2 & 1 & { - 3} \cr
3 & 4 & 1 \cr
} } \right| = A$$, then $$\left| {\...
If $${S_r} = \left| {\matrix{
{2r} & x & {n(n + 1)} \cr
{6{r^2} - 1} & y & {{n^2}(2n + 3)} \cr
{4{r^3} - 2nr} & z &am...
If the following three linear equations have a non-trivial solution, thenx + 4ay + az = 0x + 3by + bz = 0x + 2cy + cz = 0
The least positive integer n such that $${\left( {\matrix{
{\cos \pi /4} & {\sin \pi /4} \cr
{ - \sin {\pi \over 4}} & {\cos {\pi \o...
The linear system of equations$$\left. \matrix{
8x - 3y - 5z = 0 \hfill \cr
5x - 8y + 3z = 0 \hfill \cr
3x + 5y - 8z = 0 \hfill \cr} \right\}...
Let P be the set of all non-singular matrices of order 3 over R and Q be the set of all orthogonal matrices of order 3 over R. Then,
Let $$A = \left( {\matrix{
{x + 2} & {3x} \cr
3 & {x + 2} \cr
} } \right),\,B = \left( {\matrix{
x & 0 \cr
5 & {x ...
The value of det A, where $$A\, = \left( {\matrix{
1 & {\cos \theta } & 0 \cr
{ - \cos \theta } & 1 & {\cos \theta } \cr
...
Let $$A = \left( {\matrix{
1 & 1 & 1 \cr
0 & 1 & 1 \cr
0 & 0 & 1 \cr
} } \right)$$. Then, for positive intege...
Let a, b, c be such that b(a + c) $$ \ne $$ 0. If $$\left| {\matrix{
a & {a + 1} & {a - 1} \cr
{ - b} & {b + 1} & {b - 1} \cr...
Subjective
If A, B are two square matrices such that AB = A and BA = B, then prove that B2 = B.
MCQ (More than One Correct Answer)
Let $$\Delta = \left| {\matrix{
{\sin \theta \cos \phi } & {\sin \theta \sin \phi } & {\cos \theta } \cr
{\cos \theta \cos \phi } & {\cos \th...
$$\left| {\matrix{
x & {3x + 2} & {2x - 1} \cr
{2x - 1} & {4x} & {3x + 1} \cr
{7x - 2} & {17x + 6} & {12x - 1} \cr
} } \right| = 0$$ ...
Let $$A = \left[ {\matrix{
3 & 0 & 3 \cr
0 & 3 & 0 \cr
3 & 0 & 3 \cr
} } \right]$$. Then, the roots of the eq...
In a third order matrix A, aij denotes the element in the ith row and jth column. If aij = 0 for i = j= 1 for i > j= $$-$$ 1 for i < jThen the m...