Question

a non homogeneous system of three equations in three unknowns AX=d has unique solution if rank (A )=rank(AD)=​

Answer 1

Answer:

order of A

Explanation:

r(A)=r(AD)=order(A)

Answer 2

Answer:

Rank (A )=Rank(AD)=3

Explanation:

Given:

• System is non homogenous.
• Aa non homogeneous system: For AX = B, if A is non-singular, then X = A⁻¹B gives a unique solution. Then, if A is a singular matrix, that is, |A| ≠0,

$A=\left[\begin{array}{ccc}a11&a12&a13\\a21&a22&a23\\a31&a32&a33\end{array}\right]$3x3

$X=\left[\begin{array}{c}X11&X21&X31\end{array}\right]$3X1

$D=\left[\begin{array}{c}D11&D21&D31\end{array}\right]$3X1

rank (A )=rank(AD)=3