### CBSE Assignments class 09 Mathematics

Mathematics Assignments & Worksheets  For  Class IX Chapter-wise mathematics assignment for class 09. Important and useful extra questions strictly according to the CBSE syllabus and pattern with answer key CBSE Mathematics is a very good platform for the students and is contain the assignments for the students from 9 th  to 12 th  standard.  Here students can find very useful content which is very helpful to handle final examinations effectively.  For better understanding of the topic students should revise NCERT book with all examples and then start solving the chapter-wise assignments.  These assignments cover all the topics and are strictly according to the CBSE syllabus.  With the help of these assignments students can easily achieve the examination level and  can reach at the maximum height. Class 09 Mathematics    Assignment Case Study Based Questions Class IX

# Chapter 3 | Matrices

Mathematics assignment for class XII chapter 3, Extra questions with answer key on chapter 3 matrices strictly according to the CBSE syllabus and very useful for examinations.

## Mathematics Assignment On MatricesClass XII Chapter 3

Strictly according to the CBSE Syllabus

Question 1

For the matrix A = $\left [ \begin{matrix}-3 & 6 & 0 \\4 & -5 & 8 \\0 & -7 & -2 \\\end{matrix} \right ]$ , find  $\frac{1}{2}$ (A - A'), where A' is the transpose of matrix A.

Ans:   $\frac{1}{2}\left [ \begin{matrix} 0& 2 & 0 \\-2 & 0 & 15 \\0 & -15 & 0 \\\end{matrix} \right ]$

Question 2

Construct a 2 x 3 matrix whose elements in the ith row and the jth column are given by  $a_{ij}=\frac{3i-j}{2}$ .

Ans: $\left [ \begin{matrix}1 & 1/2 & 0 \\\\5/2 & 2 & 3/2 \\\end{matrix} \right ]$

Question 3

Fins a matrix X such that 2A + B + X = 0, where

A = $\left [ \begin{matrix}-1 & 2 \\3 & 4 \\\end{matrix} \right ]$   B = $\left [ \begin{matrix}3 & -2 \\1 & 5 \\\end{matrix} \right ]$

Ans:  $\left [ \begin{matrix}-1 & -2 \\-7 & -13 \\\end{matrix} \right ]$

Question 4

If A = $\left [ \begin{matrix}3 & -2 \\4 & -2 \\\end{matrix} \right ]$ , find k such that   A2 = KA – 2I

Ans:  K = 1

Question 5

Solve for x and y ;  $\left [ \begin{matrix}3 & -4 \\1 & 2 \\\end{matrix} \right ]$ $\left [ \begin{matrix}x \\y\end{matrix} \right ]$ = $\left [ \begin{matrix}3 \\11\end{matrix} \right ]$

Ans: x = 5, y = 3

Question 6

If A = $\left [ \begin{matrix}3 & -4 \\-1 & 2 \\\end{matrix} \right ]$ , find a matrix B such that AB = I

Ans:  $\left [ \begin{matrix}1 & 2 \\1/2 & 3/2 \\\end{matrix} \right ]$

Question 7

If B is a skew symmetric matrix, write whether the matrix (ABA') is symmetric or skew symmetric matrix

Ans: Skew symmetric matrix

Question 8

Show that matrix B'AB is symmetric or skew symmetric according as A is symmetric or skew symmetric matrix.

Question 9

Simplify:   $cos\theta \left [ \begin{matrix}cos\theta & sin\theta \\-sin\theta & cos\theta \\\end{matrix} \right ]$ +  $sin\theta \left [ \begin{matrix}sin\theta & -cos\theta \\cos\theta & sin\theta \\\end{matrix} \right ]$

Ans:  $\left [ \begin{matrix}1 & 0 \\0 & 1 \\\end{matrix} \right ]$

Question 10

If A = $\left [ \begin{matrix}cosx & sinx \\-sinx & cosx \\\end{matrix} \right ]$  , find x, 0 < x < π/2  , when A + A' = I

Ans:  x = π / 3

Question 11

Let A = $\left [ \begin{matrix}3 & 2 & 5 \\4 & 1 & 3 \\0 & 6 & 7 \\\end{matrix} \right ]$ , express A as sum of two matrices such as one is symmetric and other is skew symmetric.

Ans:  $\left [ \begin{matrix}3 & 3 & 5/2 \\3 & 1 & 9/2 \\5/2 & 9/2 & 7 \\\end{matrix} \right ]$ + $\left [ \begin{matrix}0 & -1 & 5/2 \\1 & 0 & -3/2 \\-5/2 & -3/2 & 0 \\\end{matrix} \right ]$

Question 12

If  A = $\left [ \begin{matrix}2 & 0 & 1 \\2 & 1 & 3 \\1 & -1 & 0 \\\end{matrix} \right ]$  , find  A2 – 5A +4I and hence find a matrix X such that A2 – 5A + 4I + X = 0

Ans:  $\left [ \begin{matrix}1 & 1 & 3 \\1 & 3 & 10 \\5 & -4 & -2 \\\end{matrix} \right ]$

Question 13

If A = $\left [ \begin{matrix}1 & 2 & 2 \\2 & 1 & 2 \\2 & 2 & 1 \\\end{matrix} \right ]$ , then show that A2 – 4A - 5I = O and hence find A-1

Ans:  A-1 =  $\frac{1}{5}\left [ \begin{matrix}-3 & 2 & 2 \\2 & -3 & 2 \\2 & 2 & -3 \\\end{matrix} \right ]$
Question 14
Find the value of x - y ; if 2 $\left [ \begin{matrix}1 & 3 \\0 & x \\\end{matrix} \right ]$ + $\left [ \begin{matrix}y & 0 \\1 & 2 \\\end{matrix} \right ]$ = $\left [ \begin{matrix}5 & 6 \\1 & 8 \\\end{matrix} \right ]$

Question 15:
If A = $\left [ \begin{matrix}8 & 0 \\4 & -2 \\3 & 6 \\\end{matrix} \right ]$  and  B = $\left [ \begin{matrix}2 & -2 \\4 & 2 \\-5 & 1 \\\end{matrix} \right ]$ , then find the value X such that  2A + X = 5B

Ans:  X = $\left [ \begin{matrix}-6 & -10 \\12 & 14 \\-31 & 7 \\\end{matrix} \right ]$

Question 16

If  $\left [ \begin{matrix}2 & 3 \\5 & 7 \\\end{matrix} \right ]$ $\left [ \begin{matrix}1 & -3 \\-2 & 4 \\\end{matrix} \right ]$ = $\left [ \begin{matrix}-4 & 6 \\-9 & x \\\end{matrix} \right ]$ , Fins x

Ans: x = 13

Question 17
If   $\left [ \begin{matrix}x & 4 & 1 \\\end{matrix} \right ]$ $\left [ \begin{matrix}2 & 1 & 2 \\1 & 0 & 2 \\0 & 2 & -4 \\\end{matrix} \right ]$ $\left [ \begin{matrix}x \\4 \\-1\end{matrix} \right ]$ = 0 , find  x

Answer : x = -2, x = -1
Question 18

If $\left [ \begin{matrix}x & x-y \\2x+y & 7 \\\end{matrix} \right ]$ = $\left [ \begin{matrix}3 & 1 \\8 & 7 \\\end{matrix} \right ]$ , then find the value of y

Question 19

If  A = $\left [ \begin{matrix}1 & 2 & 0 \\3 & -4 & 5 \\0 & -1 & 3 \\\end{matrix} \right ]$ , then Evaluate : $A^{2}$ - 4A + 3I

Answer : $\left [ \begin{matrix}6 & -14 & 10 \\-21 & 36 & -25 \\-3 & 5 & -5 \\\end{matrix} \right ]$

Question 20
Three schools X, Y, Z organized a fate (mela) for collecting funds for good victims in which they sold hand-held fans, mats and toys made from recycled material, the sale price of each being Rs 25, Rs 100 and Rs 50 respectively. The following table shows the number of articles of each type sold.

 ⟶   School  Article  ↓ X Y Z Hand-Held Fans Mats Toys 30 12 70 40 15 55 35 20 75

Using matrices, find the funds collected by each school by selling the above articles and the total funds collected.

Ans: Funds collected by school X = ₹ 5450
Funds collected by school Y = ₹ 5250
Funds collected by school Z = ₹ 6625
Total fund collected = ₹ 17325