Determinants
Exercise 4.2
Question 1: Using the property of determinants and without expanding, prove that:
Answer
= 0+0 = 0
Question 2: Using the property of determinants and without expanding, prove that:
Answer
Here, the two rows R_{1} and R_{3 }are identical.
Δ = 0.
Question 3: Using the property of determinants and without expanding, prove that:
Answer
Question 4: Using the property of determinants and without expanding, prove that:
Answer
Question 5:
Using the property of determinants and without expanding, prove that:
Answer
Hence, the given result is proved.
Question 6: By using properties of determinants, show that:
Answer
Question 7: By using properties of determinants, show that:
Answer
Question 8: By using properties of determinants, show that:
Answer
Hence, the given result is proved.
Question 9: By using properties of determinants, show that:
Answer
Question 10: By using properties of determinants, show that:
Answer
(i)
Question 11: By using properties of determinants, show that:
Answer
Question 12: By using properties of determinants, show that:
Answer
Hence, the given result is proved.
Question 13: By using properties of determinants, show that:
Answer
Question 14:
By using properties of determinants, show that:
Answer
Taking out common factors a, b, and c from respectively, we have:
Hence, the given result is proved.
Question 15: Choose the correct answer.
Answer: C
Hence, the correct answer is C.
Question 16: Which of the following is correct?
A. Determinant is a square matrix.
B. Determinant is a number associated to a matrix.
C. Determinant is a number associated to a square matrix.
D. None of these Answer
Answer: C
Thus, the determinant is a number associated to a square matrix.
Hence, the correct answer is C.
Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 