Let $T$ be the linear transformation $T$:$R^5{R}^5$ below

$T(x_1,x_2,x_3,x_4,x_5)=(x_1,-3x_2,-x_2-3x_3+x_5,x_1+x_4,x_2-3x_5)$

The characteristic polynomial of $T$ is

$(t)=(t+3{)}^3(t-1{)}^2$

In the parts below, you will compute an ordered Jordan basis $F$ and Jordan blocks for $M_F^F(T).($Click to open and close sections below$).$

Write $x_1$ as $x1$ and $x_2$ as etc.

$($A$)$ Eigenvalue $t=-3$

$(T+3)(x_1,x_2,x_3,x_4,x_5)=$

dim$(ker(T+3))=$

$(T+3{)}^2(x_1,x_2,x_3,x_4,x_5)=$

dim$(ker(T+3{)}^2)=$

$(T+3{)}^3(x_1,x_2,x_3,x_4,x_5)=$

dim$(ker(T+3{)}^3)=$

Jordan Basis $=$

Jordan Block $=\left[\begin{array}{cc}?& \end{array}\right]$

$($B$)$ Eigenvalue $t=1$

$(T-1)(x_1,x_2,x_3,x_4,x_5)=$

dim$(ker(T-1))=$

$(T-1{)}^2(x_1,x_2,x_3,x_4,x_5)=$

dim$(ker(T-1{)}^2)=$