Answer true or false to the following statement and explain your answer. A p

The following coordinates are each of a single transformation. What type of transformation occurred for image D.

Let ${\displaystyle T:P_3\left(R\right)\to M_{2\times 2}\left(R\right)}$ be a linear transformation, then find the matrix of transformation with respect to standard basis. Also, find the condition number of the matrix of transformation with respect to || ||1.

One vertex of a triangle is located at (0,5) on a coordinate grid. After a transformation, the vertex is located at (5,0). What transformations could have taken place?

Answer true or false to the following statement and explain your answer.
Any scatterplot that exhibits curvature can be straightened by the method of transformations.

Let S and T be linear transformations from V into W. Show that S + T and kT are both linear transformations, where (S + T)(v) = S(v) + T(v) and (kT)(v) = kT(v).

The solution of the initial value problem $y^{″}+4y=2\delta (t-\pi /4),y(0)=0,y^{\prime }(0)=0$ and draw the graph of the solution.

(a) identify the transformation, and
(b) graphically represent the transformation for an arbitrary vector in ${\displaystyle R_2}$.
T(x, y) = (x + 4y, y)