# EXERCISE 3.2 (MATRIX)

**Class 12 ncert solution math exercise 3.2 matrix**

**Question 1:** A= ,B=,C=

Find each of the following

(a)

(b)

(c)

(d)

(e)

**Solution:(a)**

**(b)**

**(c)**

**(d)**

**(e) **

**Question 2: Compute the following:**

**(a)**

**(b)**

**(c)**

**(d)**

**Solution: (a)**

**(b)**

**(c)**

**(d)**

**Question 3: Compute the indicated products:**

**(a)**

**(b)**

**(c)**

**(d)**

**(e)**

**(f)**

**Solution: (a)**

**(b)**

**(c)**

**(d)**

**(e)**

**(f)**

**Question 4:** If

Then compute A+B and B-C. Also, verify that A+(B+C)=(A+B)-C

**Solution: **

Hence, A+(B-C)=(A+B)-C

**Question 5:** If and

**Solution: **

**Question 6:**

**Solution:**

**Question 7: Find X and Y,if**

**(a)** and

**(b)** and

** Solution: (a) **

Adding equation (1) and (2)

Since

**(b)**

Multiplying equation (1) by 2and multiplying (2) by 3

subtracting (3) to (4)

Now,

**Question 8:**

**Solution:** Since

** Question 9:**Find x and y ,if

** Solution:** Since

Comparing the corresponding elements two matrices:

Therefore x=3 and y=3

** Question 10:** Solve the equation for x,y,z, and t if

** Solution: **

Comparing the corresponding elements two matrices:

Hence the values of x=3,y=6,z=9 and t=6

** Question 11:** If

Findthe value of x and y

**Solution: **

Comparing the corresponding elements two matrices:

Adding (1)and (2) equation

put the value of x in (1) Equation

Hence the value of x=3 and y=-4

** Question 12:** Given

Find the value of x,y,z and w.

**Solution :**

Comparing the corresponding elements two matrices:

Since

Since

Since

Therefore x=2,y=4,z=1 and w=3

**Question 13: ** If Show that .

**Solution: ** and

Now

Hence F(x)F(y)=F(x+y)

**Question 14: Show that (a)**

**(b)**

**Solution: (a)**

LHS.

RHS.

Therefore ,

**(b)**

Therefore,

**Question 15.** Find , if

**Solution:** Since

Therefore,

**Question 16:** If , Prove that

**Solution:**

Hence Proved

**Question 17: ** If and , Find k so that .

**Solution:** Since

Now

Ccmparing the corresponding element of two matrices

**Question18:** If and I is the indentity matrix of order 2 ,Show that

**Solution :**

**Question 19:** A trust fund has ₹ 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide ₹ 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of:

(a)₹ 1800 (b)₹ 2000

**Solution:** (a)

Thus, in order to obtain an annual total interest of ₹1800, the trust fund should invest ₹15000 in the first bond and the remaining ₹15000 in the second bond.

**(b)** Let ₹ x be inested in

the first bond. Then the sum of money invested in the second bond will be ₹(30000-x)

Therefore, in order to obtain an annual total interest of ₹1800, we have

Thus, in order to obtain an annual total interest of ₹2000, the trust fund should invest ₹5000 in the first bond and the remaining ₹25000 in the second bond.

**Question 20:** The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are ₹80 , ₹ 60and ₹ 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra

**Solution :**books matrix =

price matrix=

Total cost =

Thus, the bookshop will receive ₹

20160 from the sale of all these books.

Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k,

respectively. Choose the correct answer in Exercises 21 and 22.

**Question 21:** The restriction on n, k and p so that PY + WY will be defined are:

(A)k=3,p=n (B)k is arbitrary p=2

(C)p is arbitrary k=3 (D)k=2,p=3

**Solution:** Order of P=p×k

Order of Y=3×k

Order of PY=

Hence k=3

Order of W=

Order of WY=

order of PY + WY =

It is possible if p=n

and k=3

** hence option (A) is true**

**Queestion 22:**If n = p, then the order of the matrix 7X – 5Z is:

(A) p × 2 (B) 2 × n (C) n × 3 (D) p × n

**Solution:** Order of matrix X= 2× n

Order of matrix = 2× p

Order of marix or

**Hence the correct option is (B)**