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NCERT Solutions class 12 Maths Exercise 3.1 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

**Download NCERT solutions for Matrices as PDF.**

## NCERT Solutions class 12 Maths Matrices** **

**1. In the matrix A = , write:**

**(i) The order of the matrix.**

**(ii) The number of elements.**

**(iii) Write the elements **

**Ans. (i)** 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)** The number of elements in the matrix A is 3 x 4 = 12.

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

Element in second row and first column = 35

Element in third row and third column =

Element in second row and fourth column = 12

Element in second row and third column =

### NCERT Solutions class 12 Maths Exercise 3.1

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

**Ans. **Since, a matrix having element is of order

**(i)** 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)** 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. **Since, a matrix having element is of order

(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).

### NCERT Solutions class 12 Maths Exercise 3.1

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

**(i) **

**(ii) **

**(iii) **

**Ans. (i) **Given: ……….(i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

A_{2 x 2} =

**(ii)** Given: ……….(i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

A_{2 x 2} =

**(iii)** Given: ……….(i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

A_{2 x 2} =

### NCERT Solutions class 12 Maths Exercise 3.1

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

**(i) **

**(ii) **

**Ans. (i) **Given: ……….(i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

A_{3 x 4} =

**(ii)** Given: ……….(i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

Putting in eq. (i)

A_{3 x 4} =

### NCERT Solutions class 12 Maths Exercise 3.1

**6. Find the values of and from the following equations:**

**(i) **

**(ii) **

**(iii) **

**Ans. (i)**Given:

By definition of Equal matrices,

**(ii) **

Equating corresponding entries, ……….(i)

……….(ii)

And [From eq. (i), ]

or

Putting these values of in eq. (i), we have and

**(iii)** Given:

Equating corresponding entries, ……….(i)

………. (ii)

And ……….(iii)

Eq. (i) – Eq. (ii) = 9 – 5 = 4

Eq. (i) – Eq. (iii) = 9 – 7 = 2

Putting values of and in eq. (i),

### NCERT Solutions class 12 Maths Exercise 3.1

**7. Find the values of and from the equation .**

**Ans. **Equating corresponding entries,

……….(i)

……….(ii)

……….(iii)

……….(iv)

Eq. (i) – Eq. (ii) =

Putting in eq. (i),

Putting in eq. (iii),

Putting in eq. (iv),

**8. A = is a square matrix if:**

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

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

### NCERT Solutions class 12 Maths Exercise 3.1

**9. Which of the given values of and make the following pairs of matrices equal:**

** **

**(A) **

**(B) Not possible to find **

**(C) **

**(D) **

**Ans. **Equating corresponding sides,

And

Also

And

Since, values of are not equal, therefore, no values of and exist to make the two matrices equal.

Therefore, option (B) is correct.

### NCERT Solutions class 12 Maths Exercise 3.1

**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. **Since, general matrix of order 3 x 3 is

This matrix has 9 elements.

The number of choices for 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) = times =

Therefore, option (D) is correct.

## NCERT Solutions class 12 Maths Exercise 3.1

NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 13 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide

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thank u mycbseguide.com great explanation good theory simple english very very good the way of explaining was awesome and neatly highlighting the solutions great great work!!!

thank u mycbseguide.com great explanation, good theory, simple english, very very good the way of teaching .Explanation was awesome and neatly highlighting the solutions great great work!!!