If a_ij = \({1\over2}(3i-2j)\) and A = [a_ij]_2x2 is

(a)

\(\begin{bmatrix} {1\over 2}& 2 \\ -{1\over2} & 1 \end{bmatrix}\)

(b)

\(\begin{bmatrix} {1\over 2}& -{1\over2} \\ 2& 1 \end{bmatrix}\)

(c)

\(\begin{bmatrix} 2& 2\\ {1\over 2}& -{1\over2} \end{bmatrix}\)

(d)

\(\begin{bmatrix} -{1\over 2}& {1\over2} \\ 1& 2 \end{bmatrix}\)

If A = \(\begin{bmatrix}\lambda & 1 \\ -1 & -\lambda \end{bmatrix}\), then for what value of \(\lambda\), A² = O?

(a)

0

(b)

\(\pm 1\)

(c)

-1

(d)

1

The value of x, for which the matrix A = \(\begin{bmatrix} e^{x-2}& e^{7+x} \\ e^{2+x} & e^{2x+3} \end{bmatrix}\) is singular

(a)

9

(b)

8

(c)

7

(d)

6

If \(\triangle\) = \(\begin{vmatrix} a&b &c \\ x & y & z \\ p &q &r \end{vmatrix}\), then \(\begin{vmatrix} ka&kb &kc \\ kx & ky & kz \\k p &kq &kr \end{vmatrix}\) is

(a)

\(\triangle\)

(b)

k\(\triangle\)

(c)

3k\(\triangle\)

(d)

k³\(\triangle\)

If a \(\neq\) b, b, c satisfy \(\begin{vmatrix} a&2b &2c \\3 & b & c \\ 4 & a & b \end{vmatrix}=0,\) then abc =

(a)

a + b + c

(b)

0

(c)

b³

(d)

ab + bc

If \(\left\lfloor . \right\rfloor \) denotes the greatest integer less than or equal to the real number under consideration and −1\(\le\) x < 0, 0 \(\le\) y < 1, 1 \(\le\) z < 2, then the value of the determinant \(\begin{vmatrix} \left\lfloor x \right\rfloor +1& \left\lfloor y \right\rfloor & \left\lfloor z \right\rfloor \\ \left\lfloor x \right\rfloor & \left\lfloor y \right\rfloor +1& \left\lfloor z \right\rfloor \\ \left\lfloor x \right\rfloor & \left\lfloor y \right\rfloor & \left\lfloor z \right\rfloor +1\end{vmatrix}\) is

(a)

\(\left\lfloor z \right\rfloor \)

(b)

\(\left\lfloor y \right\rfloor \)

(c)

\(\left\lfloor x \right\rfloor \)

(d)

\(\left\lfloor x \right\rfloor \)+1

Let A and B be two symmetric matrices of same order. Then which one of the following statement is not true?

(a)

A + B is a symmetric matrix

(b)

AB is a symmetric matrix

(c)

AB = (BA)^T

(d)

A^T B = AB^T

If \(\begin{bmatrix} 2x+y & 4x \\ 5x-7 & 4x \end{bmatrix}=\begin{bmatrix} 7 & 7y-13 \\ y & x+6 \end{bmatrix}\), then the value of x+y is _________ .

(a)

5

(b)

6

(c)

4

(d)

3

On using elementary row operation R₁⟶R₁-3R₂ in the following matrix equation \(\begin{pmatrix} 4 & 2 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)________.

(a)

\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & -7 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

(b)

\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} -1 & -3 \\ 1 & 1 \end{pmatrix}\)

(c)

\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 1 & -7 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

(d)

\(\begin{pmatrix} 4 & 2 \\ -5 & -7 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ -3 & -3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

The value of\(\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 1+sin\theta & 1 \\ 1 & 1 & 1+cos\theta \end{matrix} \right| \) is _____________

(a)

3

(b)

1

(c)

2

(d)

\(\frac{1}{2}\)