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Consider the system of linear equations: X1 + 2X2 + X3 = 3 2x1 + 3x2 + x3 = 3 8x1 + 5x2 + 2x3 = 1 the system is ?

Consider the system of linear equations:
X1 + 2X2 + X3 = 3
2x1 + 3x2 + x3 = 3
8x1 + 5x2 + 2x3 = 1
the system is ?

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
Please find the answer to your question below
Here det A is not 0 hence rank of A=3
Also if we write augmented matrix C=[A B]
we get c=\begin{bmatrix} 1 &2 &1 &3 \\ 2& 3 &1 &3 \\ 8& 5 &2 &1 \end{bmatrix}
By doing row operations R2=R2-R1,R1=R1-R2,R3=R3-5R2
c=\begin{bmatrix} 0&1 &1 &3 \\ 1& 1 &0 &0 \\ 3& 0 &2 &1 \end{bmatrix}
so Rank of c=3
Hence the given system of equations is consistent with a unique solution

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