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Vidaara.orgClass 12 · Mathematics
CodeVID-M12-03-OPS-01
Operations on Matrices — Assignment
Chapter: Matrices
Topic: Operations on Matrices
Maximum Marks: 35
Time: 75 minutes
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.
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
2.
Matrix multiplication is, in general:
  • A.commutative
  • B.not commutative
  • C.never defined
  • D.always $O$
3.
If $AB=O$, then:
  • A.$A=O$ or $B=O$
  • B.both are $O$
  • C.neither need be $O$
  • D.$A=B$
4.
$IA$ (with $I$ identity) equals:
  • A.$O$
  • B.$A$
  • C.$2A$
  • D.$A^2$
5.
If $A=\begin{bmatrix}1&2\\3&4\end{bmatrix}$, then $2A=$
  • A.$\begin{bmatrix}2&4\\6&8\end{bmatrix}$
  • B.$\begin{bmatrix}1&2\\3&4\end{bmatrix}$
  • C.$\begin{bmatrix}2&2\\2&2\end{bmatrix}$
  • D.$\begin{bmatrix}1&4\\9&16\end{bmatrix}$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If $A=\begin{bmatrix}1&0\\2&1\end{bmatrix},\ B=\begin{bmatrix}0&1\\1&0\end{bmatrix}$, find $A+B$.
7.
Find $AB$ for $A=\begin{bmatrix}1&2\end{bmatrix},\ B=\begin{bmatrix}3\\4\end{bmatrix}$.
8.
If $A=\begin{bmatrix}2&1\\0&3\end{bmatrix}$, find $3A$.
9.
State whether $AB=BA$ in general.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
If $A=\begin{bmatrix}1&2\\3&4\end{bmatrix},\ B=\begin{bmatrix}2&0\\1&3\end{bmatrix}$, find $AB$.
11.
For the same $A,B$, find $BA$ and compare with $AB$.
12.
Find $2A-3B$ for $A=\begin{bmatrix}1&-1\\0&2\end{bmatrix},\ B=\begin{bmatrix}0&1\\1&1\end{bmatrix}$.
13.
If $A=\begin{bmatrix}1&2\\2&4\end{bmatrix},\ B=\begin{bmatrix}2&-4\\-1&2\end{bmatrix}$, find $AB$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
If $A=\begin{bmatrix}1&2\\3&4\end{bmatrix}$, find $A^2-5A$.
15.
Verify $(AB)$ is defined and find it for $A=\begin{bmatrix}1&-1&2\\0&3&1\end{bmatrix}$, $B=\begin{bmatrix}2&1\\0&1\\1&0\end{bmatrix}$.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $2\times2$
  2. (B) not commutative
  3. (C) neither need be $O$
  4. (B) $A$
  5. (A) $\begin{bmatrix}2&4\\6&8\end{bmatrix}$
Section B — Short Answer (2 marks)
  1. $\begin{bmatrix}1&1\\3&1\end{bmatrix}$.
  2. $[11]$.
  3. $\begin{bmatrix}6&3\\0&9\end{bmatrix}$.
  4. No (multiplication is not commutative).
Section C — Short Answer (3 marks)
  1. $\begin{bmatrix}4&6\\10&12\end{bmatrix}$.
  2. $BA=\begin{bmatrix}2&4\\10&14\end{bmatrix}\ne AB$.
  3. $\begin{bmatrix}2&-5\\-3&1\end{bmatrix}$.
  4. $\begin{bmatrix}0&0\\0&0\end{bmatrix}$ (zero matrix).
Section D — Long Answer (5 marks)
  1. $A^2-5A=\begin{bmatrix}2&0\\0&2\end{bmatrix}$.
  2. $AB=\begin{bmatrix}4&0\\1&3\end{bmatrix}$.
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