Matrices Test

Matrices

This is Matrices Test-02 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

If \(\left[ {\begin{array}{*{20}{c}} 0&0&0 \\ 0&0&0 \\ 1&0&0 \end{array}} \right]\)

A
none of these
B
\({A^2} = A\)
C
\({A^2} = O\)
Correct
D
\({A^3} = A\)

Let A be any \(m \times n\) matrix, then \({A^2}\) can be found only when

A
m = n
Correct
B
none of these.
C
\(m{\text{ }} > {\text{ }}n\)
D
\(\begin{array}{*{20}{l}} {m{\text{ }} < {\text{ }}n} \end{array}\)

If A and B are any two matrices, then

A
\({A^2} = O\)
B
AB = O
C
\(2{A^2}\)
D
AB may or may not be defined.
Correct

A square matrix A = \({\left[ {{a_{ij}}} \right]_{n \times n}}\) is called a lower triangular matrix if \({a_{ij}}{\text{ = }}0\) for

A
none of these.
B
i is less than j
Correct
C
iis greater than j
D
i = j

A square matrix \(A = {[{a_{ij}}]_{n \times n}}\)is called an upper triangular if \({a_{ij}} = 0\) for

A
i is less than j
B
i = j
C
none of these
D
i is greater than j
Correct

If\(\left[ {\begin{array}{*{20}{c}} 1&0 \\ 1&1 \end{array}} \right]\), then for all natural numbers n, \({A^n}\) is equal to

A
\(\left[ {\begin{array}{*{20}{c}} n&0 \\ 1&1 \end{array}} \right]\)
B
\(\left[ {\begin{array}{*{20}{c}} 1&0 \\ 1&n \end{array}} \right]\)
C
none of these.
D
\(\left[ {\begin{array}{*{20}{c}} 1&0 \\ n&1 \end{array}} \right]\)
Correct

If \(A = {[{a_{ij}}]_{2 \times 2}}\)where \({a_{ij}} = {\text{ i }} + {\text{ j}},\) then A is equal to

A
\(\left[ {\begin{array}{*{20}{c}} 2&3 \\ 3&4 \end{array}} \right]\)
Correct
B
\(\left[ {\begin{array}{*{20}{c}} 1&1 \\ 2&2 \end{array}} \right]\)
C
\(\left[ {\begin{array}{*{20}{c}} 1&2 \\ 1&2 \end{array}} \right]\)
D
\(\left[ {\begin{array}{*{20}{c}} 1&2 \\ 3&4 \end{array}} \right]\)

If \(A = \left[ {\begin{array}{*{20}{c}} 0&c&{ - b} \\ { - c}&0&a \\ b&{ - a}&0 \end{array}} \right]\)and \(B = \left[ {\begin{array}{*{20}{c}} {{a^2}}&{ab}&{ac} \\ {ab}&{{b^2}}&{bc} \\ {ac}&{bc}&{{c^2}} \end{array}} \right]\)then AB =

A
\({B^2}\)
B
0
Correct
C
\({A^3}\)
D
1

If\(A = \left[ {\begin{array}{*{20}{c}} 1&1&1 \\ 1&2&3 \\ 1&3&4 \end{array}} \right]\), thenadj (adj A)=

A
- A
Correct
B
A
C
none of these
D
\({A^2}\)

If I = \(\left[ {\begin{array}{*{20}{c}} 1&0 \\ 0&1 \end{array}} \right]\),J =\(\left[ {\begin{array}{*{20}{c}} 0&1 \\ { - 1}&0 \end{array}} \right]\)and B = \(\left[ {\begin{array}{*{20}{c}} {\cos \theta }&{\sin \theta } \\ { - \sin \theta }&{\cos \theta } \end{array}} \right]\), then B equals

A
I sin \(\theta + J\cos \theta \)
B
I cos\(\theta - Jsin\theta \)
C
- I cos\(\theta + Jsin\theta \)
D
I cos\(\theta + Jsin\theta \)
Correct

If for a matrix A, \({A^2} + I = O\)where I is the identity matrix, then A equals

A
\(\left[ {\begin{array}{*{20}{c}} i&0 \\ 0&{ - i} \end{array}} \right]\)
Correct
B
\(\left[ {\begin{array}{*{20}{c}} { - 1}&0 \\ 0&{ - 1} \end{array}} \right]\)
C
\(\left[ {\begin{array}{*{20}{c}} 1&0 \\ 0&1 \end{array}} \right]\)
D
\(\left[ {\begin{array}{*{20}{c}} 1&2 \\ { - 1}&1 \end{array}} \right]\)

If A and B are two matrices such that A + B and AB are both defined, then

A
A, B are square matrices of same order
Correct
B
number of columns of A = number of ros of B.
C
A and B can be any matrices
D
A, B are square matrices not necessarily of same order

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

A
A is non-singular
Correct
B
A is singular
C
A is symmetric
D
A is square.

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

A
both A and B are singular
B
none of these.
C
neither matrix is singular
D
either of them is singular
Correct

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

A
AB.
B
2 AB
C
2 BA
D
A + B
Correct