Given that M : (x, y) \(\to\) (7x, 3x - y) and N : (x, y) \(\to\) (2x - y; 5x + 3y)
(a) write down matrices M and N of the linear transformation
(b) find the image of P(2, -3) under the linear transformation N followed by M;
(c) find the coordinates of the point Q whose image is Q(2, 4) under the linear transformation N
(a) write down matrices M and N of the linear transformation
(b) find the image of P(2, -3) under the linear transformation N followed by M;
(c) find the coordinates of the point Q whose image is Q(2, 4) under the linear transformation N
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Correct Answer: Option
Explanation:
M = \(\begin {pmatrix} 0 & 7 \\ 3 & -1 \end {pmatrix}\)
N = \(\begin {pmatrix} 2 & -1 \\ 5 & 3 \end {pmatrix}\)
(b) p(2,-3) = (2(2) + 3, 5(2) + 3(-3))
= (7, 10 - 9) = (7, 1)
p(7, 1) = (7(1), 2(7) - 1)
= (7, 21, -1) = (7, 20)
(c) Q`(2, 4) = (2(2) - 4, 5(2) + 14)
= (4 - 4, 10 + 12)
= (0, 22)
M = \(\begin {pmatrix} 0 & 7 \\ 3 & -1 \end {pmatrix}\)
N = \(\begin {pmatrix} 2 & -1 \\ 5 & 3 \end {pmatrix}\)
(b) p(2,-3) = (2(2) + 3, 5(2) + 3(-3))
= (7, 10 - 9) = (7, 1)
p(7, 1) = (7(1), 2(7) - 1)
= (7, 21, -1) = (7, 20)
(c) Q`(2, 4) = (2(2) - 4, 5(2) + 14)
= (4 - 4, 10 + 12)
= (0, 22)