" /> -->

#### Matrices and Determinants One Mark Questions

11th Standard

Reg.No. :
•
•
•
•
•
•

Maths

Time : 00:30:00 Hrs
Total Marks : 10
10 x 1 = 10
1. If aij =${1\over2}(3i-2j)$ and A=[aij]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)

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

2. 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

3. 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

4. If A=$\begin{bmatrix} 1& 2 &2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix}$ is a matrix satisfying the equation AAT = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to

(a)

(2, - 1)

(b)

(- 2, 1)

(c)

(2, 1)

(d)

(- 2, - 1)

5. The product of any matrix by the scalar____________is the null matrix.

(a)

1

(b)

0

(c)

I

(d)

matrix itself

6. 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

7. 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)

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

8. 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)

$\frac{1}{2}$

9. 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)

$\lambda \neq \frac { -8 }{ 5 }$

10. 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