Vidaara.orgClass 12 · Mathematics
CodeVID-M12-03-TYP-01
Matrices: Order, Types & Equality — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- 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.
A scalar matrix is a special:
- A.row matrix
- B.diagonal matrix
- C.zero matrix
- D.column matrix
3.
The number of $2\times2$ matrices with entries from $\{0,1\}$ is:
- A.$8$
- B.$16$
- C.$4$
- D.$32$
4.
If $A=[a_{ij}]$ is $3\times3$ with $a_{ij}=i+j$, then $a_{23}=$
- A.$5$
- B.$6$
- C.$23$
- D.$1$
5.
A matrix that is both symmetric and skew-symmetric is:
- A.identity
- B.a zero matrix
- C.diagonal
- D.scalar
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.
Construct the $2\times2$ matrix $A=[a_{ij}]$ with $a_{ij}=2i+j$.
8.
How many entries are there in a $3\times4$ matrix?
9.
Write all possible orders of a matrix with $5$ elements.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
If a matrix has $24$ elements, list all possible orders.
11.
Find $x,y,z$ if $\begin{bmatrix}x & 2\\ z & y\end{bmatrix}=\begin{bmatrix}1 & 2\\ 3 & 4\end{bmatrix}$.
12.
Construct $A=[a_{ij}]_{2\times2}$ with $a_{ij}=\dfrac{(i+2j)^2}{2}$.
13.
How many matrices of order $2\times3$ have each entry $0$ or $1$?
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.
A matrix $A=[a_{ij}]_{3\times3}$ has $a_{ij}=1$ if $i=j$ and $0$ otherwise. Name it and write it.
Answer Key
Section A — Multiple Choice Questions
- (B) $6$
- (B) diagonal matrix
- (B) $16$
- (A) $5$
- (B) a zero matrix
Section B — Short Answer (2 marks)
- $x=4,\ y=3$.
- $\begin{bmatrix}3&4\\5&6\end{bmatrix}$.
- $12$.
- $1\times5$ and $5\times1$.
Section C — Short Answer (3 marks)
- $1\times24,2\times12,3\times8,4\times6,6\times4,8\times3,12\times2,24\times1$ (8 orders).
- $x=1,\ y=4,\ z=3$.
- $\begin{bmatrix}\tfrac92 & \tfrac{25}{2}\\[2pt] 8 & 18\end{bmatrix}$.
- $2^{6}=64$.
Section D — Long Answer (5 marks)
- $a=4,b=2$ or $a=2,b=4$.
- Identity matrix $I_3=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$.
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