Matrices Online Objective Test | Matrices Online Objective Test

# Matrices # CBSE 12th Mathematics Prepare / Learn

Q1. If

A = [a_{i j}]_{2 \times 2}

where

a_{i j} = i + j,

then A is equal to

Answer : Option A
Explaination / Solution:

If

A = [a_{i j}]_{2 \times 2}

where

a_{i j} = i + j,

then

A = [\begin{matrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{matrix}] = [\begin{matrix} 2 & 3 \\ 3 & 4 \end{matrix}]

# Matrices # CBSE 12th Mathematics Prepare / Learn

Q2. If

A = [\begin{matrix} 0 & c & - b \\ - c & 0 & a \\ b & - a & 0 \end{matrix}]

and

B = [\begin{matrix} a^{2} & a b & a c \\ a b & b^{2} & b c \\ a c & b c & c^{2} \end{matrix}]

then AB =

A. 0

B. 1

C. A3

D. B2

Answer : Option A
Explaination / Solution:

# Matrices # CBSE 12th Mathematics Prepare / Learn

Q3. If

A = [\begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 4 \end{matrix}]

then (adj A)=

A. A2

B. none of these

C. -A

D. A

Answer : Option C
Explaination / Solution:

# Matrices # CBSE 12th Mathematics Prepare / Learn

Q4.

then B equals

[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]

[\begin{matrix} 0 & 1 \\ - 1 & 0 \end{matrix}]

[\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix}]

A. - I cosθ+Jsinθ

B. I sin θ+Jcosθ

C. I cosθ−Jsinθ

D. I cosθ+Jsinθ

Answer : Option D
Explaination / Solution:

# Matrices # CBSE 12th Mathematics Prepare / Learn

Q5. If for a matrix A,

A^{2} + I = O

where I is the identity matrix, then A equals

Answer : Option D
Explaination / Solution:

# Matrices # CBSE 12th Mathematics Prepare / Learn

Q6. f A and B are two matrices such that A + B and AB are both defined, then

A. A and B can be any matrices

B. A, B are square matrices not necessarily of same order

C. number of columns of A = number of ros of B.

D. A, B are square matrices of same order

Answer : Option D
Explaination / Solution:

If A and B are square matrices of same order , both operations A + B and AB are well defined.

# Matrices # CBSE 12th Mathematics Prepare / Learn

Q7. From the matrix equation AB = AC we can conclude B = C, provided

A. A is singular matrix

B. A is square matrix

C. A is symmetric matrix

D. A is non-singular matrix.

Answer : Option D
Explaination / Solution:

Here , only non- singular matrices obey cancellation laws.

# Matrices # CBSE 12th Mathematics Prepare / Learn

Q8. If A and B are two non-zero square matrices such that AB = 0, then

A. none of these.

B. neither matrix is singular

C. both A and B are singular

D. either of them is singular

Answer : Option D
Explaination / Solution:

The product of two non-zero matrices can be a zero matrix iff one of the two given matrices should be singular.

# Matrices # CBSE 12th Mathematics Prepare / Learn

Q9.

If A and B are two matrices such that AB = BA and BA = A, then $A^{2} + B^{2} =$

A^{2} + B^{2} =

A. 2BA

B. 2AB

C. A+B

D. AB

Answer : Option C
Explaination / Solution:

# Matrices # CBSE 12th Mathematics Prepare / Learn

Q10.

[\begin{matrix} 1 & 0 \\ 1 & 1 \end{matrix}]

[\begin{matrix} - 1 & 1 \\ 1 & - 1 \end{matrix}]

A. none of these.

Answer : Option C
Explaination / Solution:

Total Question/Mark :
Scored Mark :
Mark for Correct Answer : 1
Mark for Wrong Answer : -0.5
Mark for Left Answer : 0

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