Class 12 Exam  >  Class 12 Notes  >  NCERT Solutions, Matrices, Part -3, Class 12, Maths

NCERT Solutions, Matrices, Part -3, Class 12, Maths PDF Download

Matrices and Determinants


Exercise 3.3
Question 1: Find the transpose of each of the following matrices:
matrices, mathematics, Question and Answer (Q & A)


Answer
matrices, mathematics, Question and Answer (Q & A)

 
Question 2:
matrices, mathematics, Question and Answer (Q & A)


Answer

We have

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)


Question 3:

matrices, mathematics, Question and Answer (Q & A)

Answer
matrices, mathematics, Question and Answer (Q & A)matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)


Question 4:
matrices, mathematics, Question and Answer (Q & A)


Question 5: For the matrices A and B, verify that (AB)′ = B'A' where
matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)


Question 6:

matrices, mathematics, Question and Answer (Q & A)


Answer
matrices, mathematics, Question and Answer (Q & A)


(ii)

matrices, mathematics, Question and Answer (Q & A)
matrices, mathematics, Question and Answer (Q & A)


Question 7:
matrices, mathematics, Question and Answer (Q & A)
Answer
matrices, mathematics, Question and Answer (Q & A)
matrices, mathematics, Question and Answer (Q & A)
Hence, A is a skew-symmetric matrix.


Question 8:
matrices, mathematics, Question and Answer (Q & A)
 

Answer
matrices, mathematics, Question and Answer (Q & A)

 

Question 9:
matrices, mathematics, Question and Answer (Q & A)

 

Answer

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

Question 10: Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)
matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)


Question 11: If A, B are symmetric matrices of same order, then AB − BA is a
A. Skew symmetric matrix
B. Symmetric matrix
C. Zero matrix
D. Identity matrix


Answer
The correct answer is A.
A and B are symmetric matrices, therefore, we have:

matrices, mathematics, Question and Answer (Q & A)
Thus, (AB − BA) is a skew-symmetric matrix.


Question 12:
If 
matrices, mathematics, Question and Answer (Q & A) if the value of α is

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

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FAQs on NCERT Solutions, Matrices, Part -3, Class 12, Maths

1. What are matrices in mathematics?
Ans. Matrices are rectangular arrays of numbers or symbols arranged in rows and columns. They are used to represent and manipulate data in various fields of mathematics, such as algebra, calculus, and statistics.
2. How are matrices useful in solving systems of equations?
Ans. Matrices are useful in solving systems of equations because they can be used to represent the coefficients and constants of the equations in a compact form. By performing matrix operations, such as row reduction or finding the inverse, we can solve the system of equations.
3. Can matrices be multiplied together?
Ans. Yes, matrices can be multiplied together. The product of two matrices is obtained by multiplying the corresponding elements in each row of the first matrix with the corresponding elements in each column of the second matrix, and then summing up the products.
4. What is the determinant of a matrix?
Ans. The determinant of a square matrix is a scalar value that can be calculated using a specific formula. It provides important information about the matrix, such as whether it is invertible or singular. The determinant is also used to solve systems of linear equations and find the area or volume of geometric figures.
5. How can matrices be used in computer graphics?
Ans. Matrices are extensively used in computer graphics to represent transformations, such as translation, rotation, and scaling. By applying matrix operations to the coordinates of objects or vertices, we can achieve various visual effects, such as moving, rotating, or resizing objects on a computer screen.
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