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# NCERT Solutions Exercise 4.2: Determinants - Notes | Study Mathematics (Maths) Class 12 - JEE

``` Page 1

Exercise 4.2
Question 1:
Using the property of determinants and without expanding, prove that:
Question 2:
Using the property of determinants and without expanding, prove that:
Page 2

Exercise 4.2
Question 1:
Using the property of determinants and without expanding, prove that:
Question 2:
Using the property of determinants and without expanding, prove that:
XII
Here, the two rows R1 and R3 are identical.
? = 0.
Question 3:
Using the property of determinants and without expanding, prove that:
Question 4:
Using the property of determinants and without expanding, prove that:
Page 3

Exercise 4.2
Question 1:
Using the property of determinants and without expanding, prove that:
Question 2:
Using the property of determinants and without expanding, prove that:
XII
Here, the two rows R1 and R3 are identical.
? = 0.
Question 3:
Using the property of determinants and without expanding, prove that:
Question 4:
Using the property of determinants and without expanding, prove that:
By applying C3 ? C3 + C2, we have:
Here, two columns C1 and C3 are proportional.
? = 0.
Question 5:
Using the property of determinants and without expanding, prove that:
Applying R2 ? R2 - R3, we have:
Page 4

Exercise 4.2
Question 1:
Using the property of determinants and without expanding, prove that:
Question 2:
Using the property of determinants and without expanding, prove that:
XII
Here, the two rows R1 and R3 are identical.
? = 0.
Question 3:
Using the property of determinants and without expanding, prove that:
Question 4:
Using the property of determinants and without expanding, prove that:
By applying C3 ? C3 + C2, we have:
Here, two columns C1 and C3 are proportional.
? = 0.
Question 5:
Using the property of determinants and without expanding, prove that:
Applying R2 ? R2 - R3, we have:
Applying R1 ?R3 and R2 ?R3, we have:
Applying R1 ? R1 - R3, we have:
Applying R1 ?R2 and R2 ?R3, we have:
From (1), (2), and (3), we have:
Page 5

Exercise 4.2
Question 1:
Using the property of determinants and without expanding, prove that:
Question 2:
Using the property of determinants and without expanding, prove that:
XII
Here, the two rows R1 and R3 are identical.
? = 0.
Question 3:
Using the property of determinants and without expanding, prove that:
Question 4:
Using the property of determinants and without expanding, prove that:
By applying C3 ? C3 + C2, we have:
Here, two columns C1 and C3 are proportional.
? = 0.
Question 5:
Using the property of determinants and without expanding, prove that:
Applying R2 ? R2 - R3, we have:
Applying R1 ?R3 and R2 ?R3, we have:
Applying R1 ? R1 - R3, we have:
Applying R1 ?R2 and R2 ?R3, we have:
From (1), (2), and (3), we have:
Hence, the given result is proved.
Question 6:
By using properties of determinants, show that:
We have,
Here, the two rows R1 and R3 are identical.
? = 0.
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## Mathematics (Maths) Class 12

209 videos|218 docs|139 tests

## Mathematics (Maths) Class 12

209 videos|218 docs|139 tests

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