NCERT Solutions Class 12 Maths Chapter 4 - Determinants

 Page 1


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