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NCERT Solutions Class 12 Maths Chapter 4 - Determinants

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Question 1: 
Prove that the determinant is independent of ?. 
Answer 
Hence, ? is independent of ?. 
Question 2:  
Without expanding the determinant, prove that  
Answer 
Page 2


Question 1: 
Prove that the determinant is independent of ?. 
Answer 
Hence, ? is independent of ?. 
Question 2:  
Without expanding the determinant, prove that  
Answer 
Hence, the given result is proved. 
Question 3: 
Evaluate 
Answer 
Expanding along C3, we have: 
Page 3


Question 1: 
Prove that the determinant is independent of ?. 
Answer 
Hence, ? is independent of ?. 
Question 2:  
Without expanding the determinant, prove that  
Answer 
Hence, the given result is proved. 
Question 3: 
Evaluate 
Answer 
Expanding along C3, we have: 
Question 4: 
If a, b and c are real numbers, and , 
Show that either a + b + c = 0 or a = b = c. 
Answer 
Expanding along R1, we have: 
Page 4


Question 1: 
Prove that the determinant is independent of ?. 
Answer 
Hence, ? is independent of ?. 
Question 2:  
Without expanding the determinant, prove that  
Answer 
Hence, the given result is proved. 
Question 3: 
Evaluate 
Answer 
Expanding along C3, we have: 
Question 4: 
If a, b and c are real numbers, and , 
Show that either a + b + c = 0 or a = b = c. 
Answer 
Expanding along R1, we have: 
Hence, if ? = 0, then either a + b + c = 0 or a = b = c. 
Question 5: 
Solve the equations 
Answer  
Page 5


Question 1: 
Prove that the determinant is independent of ?. 
Answer 
Hence, ? is independent of ?. 
Question 2:  
Without expanding the determinant, prove that  
Answer 
Hence, the given result is proved. 
Question 3: 
Evaluate 
Answer 
Expanding along C3, we have: 
Question 4: 
If a, b and c are real numbers, and , 
Show that either a + b + c = 0 or a = b = c. 
Answer 
Expanding along R1, we have: 
Hence, if ? = 0, then either a + b + c = 0 or a = b = c. 
Question 5: 
Solve the equations 
Answer  
Question 6: 
Prove that 
Answer 
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FAQs on NCERT Solutions Class 12 Maths Chapter 4 - Determinants

1. What is a determinant?
Ans. A determinant is a scalar value that can be calculated from a square matrix. It contains information about the matrix such as whether it is invertible or singular.
2. How do you find the determinant of a 2x2 matrix?
Ans. To find the determinant of a 2x2 matrix, you can use the formula ad - bc, where a, b, c, and d are the elements of the matrix.
3. What is the importance of determinants in linear algebra?
Ans. Determinants are important in linear algebra because they provide information about the matrix, such as whether it is invertible or singular. They are also used to solve systems of linear equations, find the area or volume of a parallelogram or parallelepiped, and calculate the eigenvalues and eigenvectors of a matrix.
4. Can the determinant of a matrix be negative?
Ans. Yes, the determinant of a matrix can be negative. The sign of the determinant depends on the number of row exchanges needed to put the matrix in row echelon form. If an odd number of row exchanges are needed, the determinant is negative; if an even number of row exchanges are needed, the determinant is positive.
5. What is the relationship between the determinant of a matrix and its inverse?
Ans. The determinant of a matrix and its inverse are related in that if the determinant is non-zero, then the matrix is invertible and its inverse can be found by dividing the adjugate (transpose of the cofactor matrix) by the determinant. If the determinant is zero, the matrix is singular and does not have an inverse.
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