- #1

karush

Gold Member

MHB

- 3,269

- 5

$$\left[\begin{array}{rrrrrrr}

1 & 0 & -1 & 0 & 1 & 0 & 3\\

0 & 1 & 0 & 0 & 1 & 0 & 1\\

0 & 0 & 0 & 1 & 4 & 0 & 2\\

0 & 0 & 0 & 0 & 0 & 1 & 3

\end{array}\right]$$

Find a basis for the null space of A, the dimension of the null space of A, and the rank of A.ok following an book example I did this $Ax=b$

$$\left[ \begin{array}{ccccccc}

1 & 0 & -1 & 0 & 1 & 0 & 3 \\

0 & 1 & 0 & 0 & 1 & 0 & 1 \\

0 & 0 & 0 & 1 & 4 & 0 & 2 \\

0 & 0 & 0 & 0 & 0 & 1 & 3

\end{array} \right]

\left[ \begin{array}{c} x_{1} \\ x_{2} \\ x_{3} \\ x_{4} \\ x_{5} \\ x_{6} \\ x_{7}

\end{array} \right]

=\left[ \begin{array}{c} 0 \\ 0 \\ 0 \\ 0

\end{array} \right]$$

which would result in

$$\begin{array}{rrrrrrr}

x_1 & &-x_3 & &x_5 & &3x_7=0 \\

&x_2 & & &x_5 & &x_7 =0\\

& & & x_4 & 4x_5 & &2x_7=0 \\

& & & & & x_6 &3x_7=0

\end{array}$$ hopefully so far !