# Class 12 ncert solution math exercise 3.2 matrix

# 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) **

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

**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:

AddingÂ (1)and (2) equation

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)**