If AX=0, Then It Has Only The Trivial Solution When?

If AX=0, then it has only the trivial solution when?

∣A∣  =0
∣A∣=0
A=0
X  =0

Explanation

If the determinant $∣ A ∣ \neq = 0$ , then $A$ is non-singular (invertible), so the homogeneous system $AX=0$ has only the trivial solution $X = 0$ .

Last updated 24-07-2026 by NA

Related MCQs

The distance of the point (2, 1) from the origin is?

√3
√5
5
None of these

اس سوال کو وضاحت کے ساتھ پڑھیں

(2³)² = ____?

2⁶
2⁵
2⁴
None of these

اس سوال کو وضاحت کے ساتھ پڑھیں

If √4x-3=4, find the value of x.

3
4
19/4
5

اس سوال کو وضاحت کے ساتھ پڑھیں

If AX=0, then it has only the trivial solution when?

∣A∣  =0
∣A∣=0
A=0
X  =0

اس سوال کو وضاحت کے ساتھ پڑھیں

Explanation

If the determinant $∣ A ∣ \neq = 0$ , then $A$ is non-singular (invertible), so the homogeneous system $AX=0$ has only the trivial solution $X = 0$ .

Last updated 24-07-2026 by NA

1/x3 +1 =(A/x+1 ) + (Bx + C/ x2-x+c) find the value of A is?

1
1/3
-1/3
0

اس سوال کو وضاحت کے ساتھ پڑھیں

Explanation

Given:

1/x ^{3} + 1 = A/ x + 1 + B x + C/ x ^{2} - x + 1

Since:

x^{3} + 1 = (x + 1) (x^{2} - x + 1)

Multiplying both sides by: $(x + 1) (x^{2} - x + 1)$ :

1 = A (x^{2} - x + 1) + (B x + C) (x + 1)

Expanding:

1 = (A + B) x^{2} + (- A + B + C) x + (A + C)

Comparing coefficients:

- A + B + C = 0

A + C = 1

A+B=0

B = - A

From $A + C = 1$ :

C = 1 - A

Substitute into the second equation:

- A - A + (1 - A) = 0

1 - 3 A = 0

A =1/ 3

Last updated on 23-07-2026 by NA

If AX=0, then it has only the trivial solution when?

Explanation

Related MCQs

اس سوال کو وضاحت کے ساتھ پڑھیں

Explanation

اس سوال کو وضاحت کے ساتھ پڑھیں

Explanation

اس سوال کو وضاحت کے ساتھ پڑھیں

Explanation

اس سوال کو وضاحت کے ساتھ پڑھیں

Explanation

اس سوال کو وضاحت کے ساتھ پڑھیں

Explanation

MCQs Categories

Latest Past Papers

Videos Lectures

If AX=0, then it has only the trivial solution when?

Explanation

Related MCQs

اس سوال کو وضاحت کے ساتھ پڑھیں

Explanation

اس سوال کو وضاحت کے ساتھ پڑھیں

Explanation

اس سوال کو وضاحت کے ساتھ پڑھیں

Explanation

اس سوال کو وضاحت کے ساتھ پڑھیں

Explanation

اس سوال کو وضاحت کے ساتھ پڑھیں

Explanation

MCQs Categories

Latest Past Papers

Videos Lectures

Sign Up

Sign In

Forgot Password