Suppose T is a transformation from <mi mathvariant="double-struck">R 2 </m

Find an explicit description of Nul A by listing vectors that span the null space.
$A=\left[\begin{array}{ccccc}1& 5& -4& -3& 1\\ 0& 1& -2& 1& 0\\ 0& 0& 0& 0& 0\end{array}\right]$

Assume that A is row equivalent to B. Find bases for Nul A and Col A.
$A=\left[\begin{array}{ccccc}1& 2& -5& 11& -3\\ 2& 4& -5& 15& 2\\ 1& 2& 0& 4& 5\\ 3& 6& -5& 19& -2\end{array}\right]$
$B=\left[\begin{array}{ccccc}1& 2& 0& 4& 5\\ 0& 0& 5& -7& 8\\ 0& 0& 0& 0& -9\\ 0& 0& 0& 0& 0\end{array}\right]$

For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A.
$A=\left[\begin{array}{cccc}2& 3& 5& -9\\ -8& -9& -11& 21\\ 4& -3& -17& 27\end{array}\right]$
Find a nonzero vector in Nul A.
$A=\left[\begin{array}{c}-3\\ 2\\ 0\\ 1\end{array}\right]$

Rotate a triangle with vertices (2, 1). (4. 1). (3, 3) by 90 degrees (clock wise) and then Translate it by Tx 4 and Ty 3 and finally rotate it by 30 degrees (anti-clock wise). (cos90=0, sin90 1. cos 30 = 0.866, sin30 =0.5)
T1 is Rotation with 90 T2 is Translation T3 is Rotation with 30
What is correct order of transformation matrix to multiply the metrix?
T3 T2 T1 or T1 T2 T3?
Should i follow the order given by the question or reverse order?

A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win 1.10; if they are different colors, then you win -1.10; if they are different colors ,then you win−1.00. (This is, you lose $1.00.) Calculate (a) the expected value of the amount you win; (b) the variance of the amount you win.

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Tell whether the system has one solution, no solution, or infinitely many solutions. Write the solutions or, if there is no solution, say the system is inconsistent. $\left[\begin{array}{cccccc}1& 2& 0& 0& |& -4\\ 0& 0& 1& 0& |& -3\\ 0& 0& 0& 1& |& 2\\ 0& 0& 0& 0& |& 0\end{array}\right]$

Solve the following pair of linear equations by the elimination method and the substitution method:
$x+y=5,2x-3y=4$