You & maths

Exercise Set 1.1 – No. 9

9. In each part, determine whether the given 3-tuple is a solution of the linear system

\large \\ 2x_1& -4x_2& -x_3& = 1 \\ x_1& -3x_2& +x_3& = 1 \\ 3x_1& -5x_2& -3x_3& = 1

\large {\color{Blue} (a) \begin{pmatrix} 3, & 1, & 1 \end{pmatrix} }

‘For each part put the values of x1, x2 and x3 a
test whether the values equals the all ones vector in RHS or not.  The matrix

\large {\color{Blue} A= \begin{bmatrix} 2 & -4 & -1 \\ 1 & -3 & 1 \\ 3 & -5 & -3 \end{bmatrix} } 

The vetor in part (a) is x=(3, 1, 1).

Ax = (1, 1, 1). Hence (3, 1, 1) is a solution.

\large {\color{Blue} (b) \begin{pmatrix} 3, & -1, & 1 \end{pmatrix} }

Ax = (9, 7, 11) # (1, 1, 1). Hence (b) is not solution.

\large {\color{Blue} (c) \begin{pmatrix} 13, & 5, & 2 \end{pmatrix} }

Ax = (4, 0, 8) # (1, 1, 1). Hence (c) is not solution.

\large {\color{Blue} (d) \begin{pmatrix} \frac{13}{2}, & \frac{5}{2}, & 2 \end{pmatrix} }

Ax = (1, 1, 1) = (1, 1, 1). Hence (d) is a solution.

\large {\color{Blue} (e) \begin{pmatrix} 17, & 7, & 5 \end{pmatrix} }

Ax = (1, 1, 1) = (1, 1, 1). Hence (e) is a solution.