# NCERT Solutions, Determinants, Part -7, Class 12, Maths Notes - Class 12

## Class 12: NCERT Solutions, Determinants, Part -7, Class 12, Maths Notes - Class 12

The document NCERT Solutions, Determinants, Part -7, Class 12, Maths Notes - Class 12 is a part of Class 12 category.
All you need of Class 12 at this link: Class 12

Determinants

Miscellaneous Solutions

Question 1:
Prove that the determinant
is independent of θ.

Hence, Δ is independent of θ.

Question 2: Without expanding the determinant, prove that

Hence, the given result is proved.

Question 3: Evaluate

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.

Expanding along R1, we have:

Hence, if Δ = 0, then either a + b + c = 0 or a = b = c.

Question 5: Solve the equations

Question 6: Prove that

Expanding along R3, we have:

Hence, the given result is proved.

Question 8: Let verify that

Question 9: Evaluate

Expanding along R1, we have:

Question 10: Evaluate

Question 11: Using properties of determinants, prove that:

Hence, the given result is proved.

Question 12: Using properties of determinants, prove that:

Expanding along R3, we have:

Hence, the given result is proved.

Question 13: Using properties of determinants, prove that:

Hence, the given result is proved.

Question 14: Using properties of determinants, prove that:

Hence, the given result is proved.

Question 15: Using properties of determinants, prove that:

Hence, the given result is proved.

Question 16: Solve the system of the following equations

This system can be written in the form of AX = B, where

Question 17: Choose the correct answer. If a, b, c, are in A.P., then the determinant

A. 0

B. 1

C. x

D. 2x

Here, all the elements of the first row (R1) are zero.
Hence, we have Δ = 0.

Question 18: Choose the correct answer. If x, y, z are nonzero real numbers, then the inverse of matrix

is
A.

B.
C.

D.

Question 19: Choose the correct answer.
Let
, where 0 ≤ θ≤ 2π, then
A). Det (A) = 0
B). Det (A) (2, ∞)
C). Det (A) (2, 4)
D). Det (A) [2, 4]

The document NCERT Solutions, Determinants, Part -7, Class 12, Maths Notes - Class 12 is a part of Class 12 category.
All you need of Class 12 at this link: Class 12
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