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)

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

Which one of the following is not true about the matrix \(\begin{bmatrix} 1 &0 &0 \\ 0 & 0 &0 \\ 0 & 0 & 5 \end{bmatrix}?\)

(a)

a scalar matrix

(b)

a diagonal matrix

(c)

an upper triangular matrix

(d)

a lower triangular matrix

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

If A =\(\begin{bmatrix} 1& 2 &2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix}\) is a matrix satisfying the equation AA^T = 9I, where I is 3 \(\times\) 3 identity matrix, then the ordered pair (a, b) is equal to

(a)

(2, - 1)

(b)

(- 2, 1)

(c)

(2, 1)

(d)

(- 2, - 1)

The product of any matrix by the scalar_________is the null matrix.

(a)

1

(b)

0

(c)

I

(d)

matrix itself

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)

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

If \(\left( \begin{matrix} 2 & \lambda & -3 \\ 0 & 2 & 5 \\ 1 & 1 & 3 \end{matrix} \right) \) is a singular matrix, then \(\lambda \) is_____________

(a)

\(\lambda \)=2

(b)

\(\lambda \)≠2

(c)

\(\lambda =\frac { -8 }{ 5 } \)

(d)

\(\lambda \neq \frac { -8 }{ 5 } \)

If f(x) = \(\left| \begin{matrix} 0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0 \end{matrix} \right| \)  then _____________

(a)

f(a) = 0

(b)

f(b) = 0

(c)

f(0) = 0

(d)

f(1) = 0