Let A = {bmatrix} 2 & -1 & 3 \\ 1 & 1 & -1 \\ 0 & 0 & 1 {bmatrix} and {bmatrix} 0 \\ 1 \\ 0 {bmatrix}. The system AX=D has

Correct Answer is : A unique solution

Correct Answer is : A unique solution

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AP EAMCET Engineering 22 Sep 2020 Shift 2 Paper

Section: Mathematics

Question : 29 of 160

Marks: +1, -0

Let

A

\begin{bmatrix} 2 & -1 & 3 \\ 1 & 1 & -1 \\ 0 & 0 & 1 \end{bmatrix}

\begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix}

AX=D

has

Solution:

A=\begin{bmatrix} 2 & -1 & 3 \\ 1 & 1 & -1 \\ 0 & 0 & 1 \end{bmatrix} D=\begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix}

Given,

A X=D

\begin{bmatrix} 2 & -1 & 3 \\ 1 & 1 & -1 \\ 0 & 0 & -1 \end{bmatrix}\begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix}

2x+y-z=1

x-y+3z=0

0x+0y-z=0

\Delta=\begin{vmatrix} 2 & -1 & 3 \\ 1 & 1 & -1 \\ 0 & 0 & -1 \end{vmatrix}

=2(-1+0)+1(-1+0)+3

=-2-1

\Delta=-3 \neq 0

\therefore

System of equations have unique solution.

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