# Â 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)Â

(d)Â

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:Â

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

Question 5: If and

Solution:Â

Question 6:

Solution:

Question 7: Find X and Y,if

(a) and

(b) and

Â Solution: (a)

Since

(b)

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

subtracting (3) to (4)

Now,

Question 8:

Solution: Since

Â QuestionÂ  9:Find x and y ,ifÂ

Â Solution: Since

Comparing the corresponding elements two matrices:

Therefore x=3 and y=3

Â Question 10: Solve the equationÂ  for x,y,z, and t if

Â  Solution:

Comparing the corresponding elements two matrices:

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

Â  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

Â  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:Â Â  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 , ProveÂ  thatÂ

Solution:

Hence Proved

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

Solution: Since

Now

Ccmparing the correspondingÂ  element ofÂ  two matrices

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

Solution :

Question 19: A trust fund hasÂ  â‚¹ 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 â‚¹ 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of:

(a)â‚¹ 1800Â Â Â Â Â  (b)â‚¹ 2000

Solution: (a)

Thus, in order to obtain an annual total interest of â‚¹1800, the trust fund should investÂ  â‚¹15000 in the first bond and the remaining â‚¹15000 in the second bond.

(b) LetÂ  â‚¹ x be inested in

the first bond. Then the sum of money invested in the second bond will beÂ  â‚¹(30000-x)

Therefore, in order to obtain an annual total interest of â‚¹1800, we have

Thus, in order to obtain an annual total interest of â‚¹2000, the trust fund should investÂ  â‚¹5000 in the first bond and the remaining â‚¹25000 in the second bond.

Question 20: The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10Â  dozen economics books. Their selling prices are â‚¹80 , â‚¹ 60and â‚¹ 40 each respectively. Find theÂ  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 â‚¹

20160 from the sale of all these books.

Assume X, Y, Z, W and P are matrices of order 2 Ã— n, 3 Ã— k, 2 Ã— p, n Ã— 3 and p Ã— 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=nÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (B)k is arbitrary p=2

(C)p is arbitrary k=3Â Â  (D)k=2,p=3

Solution: Order of P=pÃ—k

Order of Y=3Ã—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

Â  hence option (A) is true

Queestion 22:If n = p, then the order of the matrix 7X â€“ 5Z is:

(A) p Ã— 2 (B) 2 Ã— n (C) n Ã— 3 (D) p Ã— n

Solution: Order of matrix X=Â  2Ã— n

OrderÂ  ofÂ  matrix = 2Ã— p

Order of marixÂ  or

Hence theÂ  correct option is (B)