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If A and B are two symmetric matrices of the same order. Then, the matrix AB – BA is equal to

1) a symmetric matrix 2) a skew-symmetric matrix 3) a null matrix 4) the identity matrix Solution: (2) a skew-symmetric matrix A and B are... View Article

If A is a square matrix, then

1) A + AT is symmetric 2) AAT is skew-symmetric 3) AT + A is skew-symmetric 4) AT is skew-symmetric Solution: (1) A + AT is symmetric (A +... View Article

Let 𝞈 = (- 1 / 2) + i (√3 / 2), then the value of the determinant [latex]\begin{vmatrix} 1 &1 &1 \\ 1&-1-\omega^{2} &\omega^{2} \\ 1& \omega^{2} & \omega \end{vmatrix}[/latex] is

1) 3ω 2) 3ω (ω - 1) 3) 3ω2 4) 3ω (1 - ω) Solution: (2) 3ω (ω - 1)... View Article

If [latex]A=\begin{bmatrix} x &1 \\ 1&0 \end{bmatrix}[/latex] and A² is the identity matrix, then x =

1) –1 2) 0 3) 1 4) 2 Solution: (2) 0... View Article

If A^T and B^T are transpose matrices of the square matrices A and B respectively then (AB)^T is equal to

1) AT BT 2) ABT 3) BAT 4) BT AT Solution: (4) BT AT AT and BT are transpose matrices of A and B respectively (AB)T = BT AT [From the... View Article

If A = [aij]_2×2, where a_ij = i + j, then A is equal to

1) 2) 3) 4) Solution: (4)... View Article

If the matrices [latex]A=\begin{bmatrix} 2 &1 &3 \\ 4&1 &0 \end{bmatrix},B=\begin{bmatrix} 1 &-1 \\ 0&2 \\ 5&0 \end{bmatrix}[/latex] then AB will be

1) 2) 3) 4) Solution: (1)... View Article

If [latex]\begin{bmatrix} x-y-z\\ -y+z\\ z \end{bmatrix}=\begin{bmatrix} 0\\ 5\\ 3 \end{bmatrix}\\[/latex] then x, y and z are

1) 5 , 2 , 2 2) 1 , - 2 , 3 3) 0 , - 3 , 3 4) 11 , 8 , 3 5) 4 , 1 , 3 Solution: (2) 1 , - 2 , 3... View Article

If the system of equations x – ky – z = 0, kx – y – z = 0, x + y – z = 0 has a non-zero solution, then the possible values of k are

1) –1, 2 2) 1, 2 3) 0, 1 4) –1, 1 Solution: (4) –1, 1... View Article

If [latex]A=\begin{bmatrix} 3 &x-1 \\ 2x+3&x+2 \end{bmatrix}[/latex] is a symmetric matrix, then the value of x is

1) 4 2) 3 3) - 4 4) - 3 Solution: (3) - 4... View Article

If A = [latex]\begin{bmatrix} 1 &2 &2 \\ 2&1 &-2 \\ a&2 &b \end{bmatrix}[/latex] is a matrix satisfying AA^T = 9I₃ then the values of a and b are

1) 1 , 2 2) - 1 , 2 3) - 1 , - 2 4) 2 , 1 5) - 2 , - 1 Solution: (5) - 2 , - 1... View Article

[latex]A=\begin{bmatrix} 1 &0 &0 \\ 0&1 &1 \\ 0&-2 &4 \end{bmatrix},I=\begin{bmatrix} 1 &0 &0 \\ 0&1 &0 \\ 0&0 &1 \end{bmatrix},A^{-1}=[(1/6)(A^{2}+cA+dI)][/latex], then the value of c and d are

1) (–6, –11) 2) (6, 11) 3) (–6, 11) 4) (6, –11) Solution: (3) (–6, 11)... View Article

If A and B are two symmetric matrices of order 3. Statement I A(BA) and (AB) A are symmetric matrices. Statement II AB is a symmetric matrix If matrix multiplication of A and B is commutative.

1) Statement I is correct, Statement II is correct; Statement II is not a correct explanation for the statement I 2) Statement I is correct,... View Article

If M is a 3 × 3 matrix satisfying [latex]M\begin{bmatrix} 0\\ 1\\ 0 \end{bmatrix}=\begin{bmatrix} -1\\ 2\\ 3 \end{bmatrix},M\begin{bmatrix} 1\\ -1\\ 0 \end{bmatrix}=\begin{bmatrix} 1\\ 1\\ -1 \end{bmatrix},M\begin{bmatrix} 1\\ 1\\ 1 \end{bmatrix}=\begin{bmatrix} 0\\ 0\\ 12 \end{bmatrix}[/latex], then the sum of the diagonal entries of M is

1) 9 2) 8 3) 10 4) 11 Solution: (1) 9... View Article

The parameter, on which the value of the determinant [latex]\begin{vmatrix} 1 &a &a^{2} \\ cos (p-d)x&cospx &cos(p+d)x \\ sin (p-d)x&sinpx &sin(p+d)x \end{vmatrix}[/latex] does not depend upon is

1) a 2) p 3) d 4) x Solution: 2) p... View Article

If ω is a complex cube root of unity with ω ≠ 1 and p = [pij] is a n × n matrix with P_ij = ω^{i + j}. Then P² ≠ 0 when n is equal to

1) 55 2) 58 3) 56 4) All of these Solution: (4) All of these P = [Pij]nxm; Pij = wi+j If n = 1, then [Pij]1x1 = [w2] = P P = w2 P2 = w4... View Article

If P is a 3 × 3 matrix such that P^T = 2P + I, where P^T is the transpose of P and I is the 3 × 3 identity matrix, then there exists a column matrix, [latex]X=\begin{bmatrix} x\\ y\\ z \end{bmatrix}\neq\begin{bmatrix} 0\\ 0\\ 0 \end{bmatrix}[/latex] such that

1) 2) PX 3) PX = 2X 4) PX = - X Solution: (4) PX = - X PT = 2P + I (PT)T = (2P + I)T + IT = 2PT + I P = 2PT + I P = 2 (2P + I) + I = 4P +... View Article

Compute [latex]\begin{bmatrix} 1 &3 &0 \\ 2&1 &4 \end{bmatrix} \times \begin{bmatrix} 1 &3 \\ 0&2 \\ -2&-1 \end{bmatrix}[/latex]

1) 2) 3) 4) Solution: (3)... View Article

If A = [latex]\begin{bmatrix} 2 &-1 \\ 1&2 \end{bmatrix}[/latex] then A² + 2A – 3I =

1) 2) 0 3) 4) 5I Solution: (1)... View Article

If A and B are square matrices of equal degree, then which one is correct among the following?

1) A + B = B + A 2) A + B = A – B 3) A – B = B – A 4) AB = BA Solution: (1) A + B = B + A If A and B are square matrices of equal degree,... View Article

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