The function L is a linear transformation function of vectors given by L(v) = Av , where20  A =   1 −1and av = a b, =   b. Which of the following is the image of −2, 3 under the linear transformation L ?(A) 1, −3(B) −4, −5(C) −4, −3(D) −4, 0

The linear transformation of a vector under a given matrix involves multiplying the matrix by the vector. In this case, we have:

A = [20, 1; -1, -1] and v = [-2; 3]

We find the image of v under the transformation L by multiplying A and v:

L(v) = A * v

This results in a new vector:

L(v) = [20, 1; -1, -1] * [-2; 3]

To multiply a matrix by a vector, we multiply each element of the first row of the matrix by the corresponding element of the vector, and add the results to get the first element of the new vector. We repeat this process for the second row:

L(v) = [(20*-2) + (13); (-1-2) + (-1*3)] = [-40 + 3; 2 - 3] = [-37; -1]

So, the image of the vector [-2; 3] under the linear transformation L is [-37; -1]. This option is not listed in the given choices (A, B, C, D). Please check the problem statement again.

The image of a vector under a linear transformation is found by multiplying the transformation matrix by the vector. In this case, the transformation matrix A is given by:

A = [20, 1] [-1, -1]

and the vector v is given by:

v = [-2] [3]

We multiply A by v to find the image of v under the transformation L:

L(v) = Av = [20, 1] * [-2] [-1, -1] [3] = [20*(-2) + 13] [-1(-2) - 1*3] = [-40 + 3] [2 - 3] = [-37] [-1]

So, the image of the vector (-2, 3) under the linear transformation L is (-37, -1). This option is not listed in the given choices (A, B, C, D). There might be a mistake in the problem or the provided options.