# 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)

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:

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)