Use matrix multiplication to find The reflection of (1 1 -3) about the y-axis Th

Question

Use matrix multiplication to find The reflection of (1 1 -3) about the y-axis The orthogonal projection of (1 1 0) onto the xy plane The orthogonal projection of (1 -2 3) onto the z axis The rotation of (1 -2 3) around the z-axis by 30 clockwise The rotation of (1 -2 3) around the z-axis by 30 clockwise followed by contraction with factor 2, followed by projection onto x = 0 plane. What is the standard matrix for the stated composition? The orthogonal projection of (1 -2 3) onto the z-axis followed by dilation with factor 2, followed by rotation around x axis by 90 . What is the Standard matrix for the stated composition?

Explanation / Answer

a) reflection of (1 , 1, -3) about y-axis is (-1,1,3)

b) since the point is on the x-y plane orthogonal projection onto it is zero

c) orthogonal projection of(1,1,0) onto z-axix is

(1^2 + 1^2)^0.5 = 1.414

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