Lecture 7 : Revision

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]

Choose the correct answer.

If x, y, z are nonzero real numbers, then the inverse of matrix is

A.  B. 

C.  D. 

Choose the correct answer.

If a, b, c, are in A.P., then the determinant

A. 0 B. 1 C. x D. 2x

Solve the system of the following equations

Using properties of determinants, prove that:

Using properties of determinants, prove that:

Using properties of determinants, prove that:

Using properties of determinants, prove that:

Using properties of determinants, prove that:

Evaluate 

Evaluate 

:  

Let verify that

(i) 

(ii) 

If 

Prove that 

Solve the equations 

If a, b and c are real numbers, and,

Show that either a + b + c = 0 or a = b = c.

Evaluate 

Without expanding the determinant, prove that

Prove that the determinant is independent of θ.