WB JEE
Mathematics
Matrices and Determinants
Previous Years Questions

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...
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