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Vidaara.orgClass 12 · Mathematics
CodeVID-M12-03-CT
Matrices — Full Chapter Test
Chapter: Matrices
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
A matrix with $20$ elements can have how many distinct orders?
  • A.$4$
  • B.$6$
  • C.$5$
  • D.$10$
2.
If $A$ is $2\times3$ and $B$ is $3\times2$, the order of $AB$ is:
  • A.$2\times2$
  • B.$3\times3$
  • C.$2\times3$
  • D.undefined
3.
$(AB)^{T}=$
  • A.$A^{T}B^{T}$
  • B.$B^{T}A^{T}$
  • C.$AB$
  • D.$BA$
4.
A scalar matrix is a special:
  • A.row matrix
  • B.diagonal matrix
  • C.zero matrix
  • D.column matrix
5.
Matrix multiplication is, in general:
  • A.commutative
  • B.not commutative
  • C.never defined
  • D.always $O$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If $\begin{bmatrix}x+y & 5\\ 0 & x-y\end{bmatrix}=\begin{bmatrix}7 & 5\\ 0 & 1\end{bmatrix}$, find $x,y$.
7.
If $A=\begin{bmatrix}1&0\\2&1\end{bmatrix},\ B=\begin{bmatrix}0&1\\1&0\end{bmatrix}$, find $A+B$.
8.
Find $A^{T}$ for $A=\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}$.
9.
Construct the $2\times2$ matrix $A=[a_{ij}]$ with $a_{ij}=2i+j$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
If a matrix has $24$ elements, list all possible orders.
11.
If $A=\begin{bmatrix}1&2\\3&4\end{bmatrix},\ B=\begin{bmatrix}2&0\\1&3\end{bmatrix}$, find $AB$.
12.
Express $A=\begin{bmatrix}2&3\\1&4\end{bmatrix}$ as a sum of a symmetric and a skew-symmetric matrix.
13.
Find $x,y,z$ if $\begin{bmatrix}x & 2\\ z & y\end{bmatrix}=\begin{bmatrix}1 & 2\\ 3 & 4\end{bmatrix}$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
If $\begin{bmatrix}a+b & 2\\ 5 & ab\end{bmatrix}=\begin{bmatrix}6 & 2\\ 5 & 8\end{bmatrix}$, find $a$ and $b$.
15.
If $A=\begin{bmatrix}1&2\\3&4\end{bmatrix}$, find $A^2-5A$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $6$
  2. (A) $2\times2$
  3. (B) $B^{T}A^{T}$
  4. (B) diagonal matrix
  5. (B) not commutative
Section B — Short Answer (2 marks)
  1. $x=4,\ y=3$.
  2. $\begin{bmatrix}1&1\\3&1\end{bmatrix}$.
  3. $\begin{bmatrix}1&4\\2&5\\3&6\end{bmatrix}$.
  4. $\begin{bmatrix}3&4\\5&6\end{bmatrix}$.
Section C — Short Answer (3 marks)
  1. $1\times24,2\times12,3\times8,4\times6,6\times4,8\times3,12\times2,24\times1$ (8 orders).
  2. $\begin{bmatrix}4&6\\10&12\end{bmatrix}$.
  3. $\begin{bmatrix}2&2\\2&4\end{bmatrix}+\begin{bmatrix}0&1\\-1&0\end{bmatrix}$.
  4. $x=1,\ y=4,\ z=3$.
Section D — Long Answer (5 marks)
  1. $a=4,b=2$ or $a=2,b=4$.
  2. $A^2-5A=\begin{bmatrix}2&0\\0&2\end{bmatrix}$.
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