## NCERT Solutions for Class 12 Maths Exercise 3.1 Chapter 3 â€“ Matrices â€“ FREE PDF Download

NCERT Class 12 Maths Ch 3 is one of the most important ones in the NCERT syllabus. Duly following NCERT Solutions for Class 12 Maths Chapter 3 ensures you that there will be no hindrance when you opt for more advanced branches of Maths. Class 12 Maths Chapter 3 â€“ Matrices solved by Expert Teachers as per NCERT (CBSE) Book guidelines. All Matrices Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks.

# NCERT Solutions for Class 12 Maths Chapter Chapter 3 â€“ Matrices

1. In the matrix A =Â
, write:

(i) The order of the matrix.

(ii) The number of elements.

(iii) Write the elementsÂ a13,a21,a33,a24,a23a13,a21,a33,a24,a23

Therefore, Order of the matrix is 3 x 4.

(ii)Â The number of elements in the matrix A is 3 x 4 = 12.

(iii)Â Â Element in first row and third column = 19

Â Element in second row and first column = 35

Â Element in third row and third column =Â

Â Element in second row and fourth column = 12

Â Element in second row and third column =Â

(i) The order of the matrix.

(ii) The number of elements.

(iii) Write the elementsÂ a13,a21,a33,a24,a23a13,a21,a33,a24,a23

**Ans.**Â (i)Â There are 3 horizontal lines (rows) and 4 vertical lines (columns) in the given matrix A.

Therefore, Order of the matrix is 3 x 4.

(ii)Â The number of elements in the matrix A is 3 x 4 = 12.

(iii)Â Â Element in first row and third column = 19

Â Element in second row and first column = 35

Â Element in third row and third column =Â

Â Element in second row and fourth column = 12

Â Element in second row and third column =Â

### 2. If a matrix has 24 elements, what are possible orders it can order? What, if it has 13 elements?

**Ans.**Â Since, a matrix havingÂ Â element is of orderÂ

(i)Â Therefore, there are 8 possible matrices having 24 elements of orders 1 x 24, 2 x 12, 3 x 8, 4 x 6, 24 x 1, 12 x 2, 8 x 3, 6 x 4.

(ii)Â Prime number 13 = 1 x 13 and 13 x 1

Therefore, there are 2 possible matrices of order 1 x 13 (Row matrix) and 13 x 1 (Column matrix).

### 3. If a matrix has 18 elements, what are the possible orders it can have? What if has 5 elements?

**Ans.**Â Since, a matrix havingÂ Â element is of orderÂ

(i) Therefore, there are 6 possible matrices having 18 elements of orders 1 x 18, 2 x 9, 3 x 6, 18 x 1, 9 x 2, 6 x 3.

(ii) Prime number 5 = 1 x 5 and 5 x 1

Therefore, there are 2 possible matrices of order 1 x 5 (Row matrix) and 5 x 1 (Column matrix).

### 4. Construct a 2 x 2 matrix A =Â Â whose elements are given by:

(i)Â

(ii)Â

(iii)Â

**Ans.**Â (i)Â Given:Â Â Â â€¦â€¦â€¦.(i)

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

Â A

_{2 x 2}Â =Â

(ii)Â Given:Â â€¦â€¦â€¦.(i)

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

Â A

_{2 x 2}Â =Â

(iii)Â Given:Â Â â€¦â€¦â€¦.(i)

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

Â A

_{2 x 2}Â =Â

### 5. Construct a 3 x 4 matrix, whose elements are given by:

(i)Â

(ii)Â

**Ans.**Â (i)Â Given:Â Â â€¦â€¦â€¦.(i)

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

Â A

_{3 x 4}Â =Â

(ii)Â Given:Â Â â€¦â€¦â€¦.(i)

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

PuttingÂ Â in eq. (i)Â

Â A

_{3 x 4}Â =Â

### 6. Find the values ofÂ Â andÂ Â from the following equations:

(i)Â

(ii)Â

(iii)Â

**Ans.**Â (i)Given:Â Â

By definition of Equal matrices,Â

(ii)Â

Equating corresponding entries,Â Â â€¦â€¦â€¦.(i)

Â Â Â Â â€¦â€¦â€¦.(ii)

AndÂ Â Â Â [From eq. (i),Â ]

Â

Â

Â

Â Â orÂ

Putting these values ofÂ Â in eq. (i), we haveÂ Â andÂ

Â Â Â or x = 4, y=2, z=0

(iii)Â Given:Â Â

Equating corresponding entries,Â Â â€¦â€¦â€¦.(i)

Â â€¦â€¦â€¦. (ii)

AndÂ â€¦â€¦â€¦.(iii)

Eq. (i) â€“ Eq. (ii) =Â Â 9 â€“ 5 = 4

Eq. (i) â€“ Eq. (iii) =Â Â 9 â€“ 7 = 2

Putting values ofÂ Â andÂ Â in eq. (i),

Â Â Â

Â Â

### 7. Find the values ofÂ Â andÂ Â from the equationÂ .

**Ans.**Â Equating corresponding entries,

Â â€¦â€¦â€¦.(i)

Â â€¦â€¦â€¦.(ii)

Â â€¦â€¦â€¦.(iii)

Â â€¦â€¦â€¦.(iv)

Eq. (i) â€“ Eq. (ii) =Â

Â

PuttingÂ Â in eq. (i),Â Â

Â Â Â Â

PuttingÂ Â in eq. (iii),Â

Â Â Â Â

PuttingÂ Â in eq. (iv),Â

Â Â Â Â

Â Â

### 8. A =Â Â is a square matrix if:

(A)Â Â (B)Â Â (C)Â Â (D) None of these

**Ans.**Â By definition of square matrixÂ , option (C) is correct.

### 9. Which of the given values ofÂ Â andÂ Â make the following pairs of matrices equal:

(A)Â

(B) Not possible to find

(C)Â

(D)Â

**Ans.**Â Equating corresponding sides,

Â Â Â

AndÂ Â

AlsoÂ Â

AndÂ

Since, values ofÂ Â are not equal, therefore, no values ofÂ Â andÂ Â exist to make the two matrices equal.

Therefore, option (B) is correct.

### 10. The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is:

(A) 27

(B) 18

(C) 81

(D) 512

**Ans.**Â Since, general matrix of order 3 x 3 isÂ

This matrix has 9 elements.

The number of choices forÂ Â is 2 (as 0 or 1 can be used)

Similarly, the number of choices for each other element is 2.

Therefore, total possible arrangements (matrices) =Â Â times =Â

Therefore, option (D) is correct.