Question

Vector v, represented as a column matrix [4−2] is transformed using the transformation matrix [0−110].

What is the transformed vector?

Responses

[46]
left square bracket. first row. 4. second row. 6. right square bracket.

[2−4]
left square bracket. first row. 2. second row. negative 4. right square bracket.

[26]
left square bracket. first row. 2. second row. 6. right square bracket.

[−2−4]

Answer 1

Compute T v with T = [[0, −1], [1, 0]] and v = [4; −2]:

T v = [0*4 + (−1)*(−2); 1*4 + 0*(−2)] = [2; 4].

So the transformed vector is [2; 4]. None of the four response choices given matches that result — please check the listed options or the transformation matrix.