$2.$ Let

A $=$

$$

$$

$123$

$459$

$6713$

$$

$.$

$($a$)$ Find the reduced row echelon form of A$.$

$($b$)$ Find the rank, rank$($A$),$ of the matrix A$.$

$($c$)$ Find the coefficients c$1,$ c$2,$ c$3,$ not all equal to zero, such that

c$1$

$$

$$

$1$

$4$

$6$

$$

$+$ c$2$

$$

$$

$2$

$5$

$7$

$$

$+$ c$3$

$$

$$

$3$

$9$

$13$

$$

$=$

$->0.$

$($d$)$ Find the coefficients d$1,$ d$2,$ d$3,$ not all equal to zero, such that

d$1$

$$

$$

$1$

$2$

$3$

$$

$+$ d$2$

$$

$$

$4$

$5$

$9$

$$

$+$ d$3$

$$

$$

$6$

$7$

$13$

$$

$=$

$->0.$

$($e$)$ Are the following statements true or false? Please justify your answer by referring to the definitions.

i$.$ The set of vectors containing the columns of A is linearly dependent.

ii$.$ The set of vectors containing the rows of A is linearly dependent.