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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-15-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.
The order is written as:
  • A.columns $\times$ rows
  • B.rows $\times$ columns
  • C.rows $+$ columns
  • D.product
2.
Two matrices can be added if they have the:
  • A.same order
  • B.same rows only
  • C.product defined
  • D.same first entry
3.
Matrices are added:
  • A.row by column
  • B.element by element
  • C.by determinants
  • D.by transposing
4.
A $2\times3$ matrix has:
  • A.$5$
  • B.$6$
  • C.$8$
  • D.$23$
5.
For $AB$ to exist:
  • A.rows of $A$ $=$ rows of $B$
  • B.columns of $A$ $=$ rows of $B$
  • C.$A=B$
  • D.both square
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
State the order of a matrix with $3$ rows and $4$ columns.
7.
Can a $2\times2$ and a $2\times2$ matrix be added?
8.
Find $\begin{bmatrix}1&2\end{bmatrix}+\begin{bmatrix}3&4\end{bmatrix}$.
9.
How many elements are in a $4\times2$ matrix?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
A matrix has $12$ elements. List all possible orders.
11.
State the condition for two matrices to be conformable for addition.
12.
If $A=\begin{bmatrix}1&2\\3&4\end{bmatrix},\ B=\begin{bmatrix}0&1\\1&0\end{bmatrix}$, find $A+B$.
13.
How many elements are in a $3\times3$ matrix?
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A matrix has $18$ elements. Write all possible orders.
15.
Given $A$ of order $3\times4$ and $B$ of order $4\times3$, state the orders of $AB$ and $BA$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) rows $\times$ columns
  2. (A) same order
  3. (B) element by element
  4. (B) $6$
  5. (B) columns of $A$ $=$ rows of $B$
Section B — Short Answer (2 marks)
  1. $3\times4$.
  2. Yes.
  3. $\begin{bmatrix}4&6\end{bmatrix}$.
  4. $8$.
Section C — Short Answer (3 marks)
  1. $1\times12,2\times6,3\times4,4\times3,6\times2,12\times1$.
  2. They must have the same order.
  3. $\begin{bmatrix}1&3\\4&4\end{bmatrix}$.
  4. $9$.
Section D — Long Answer (5 marks)
  1. $1\times18,2\times9,3\times6,6\times3,9\times2,18\times1$.
  2. $AB$ is $3\times3$; $BA$ is $4\times4$.
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