Find the matrix of a relflection at y=-4x.(adsbygoogle = window.adsbygoogle || []).push({});

I found out that b1 = [1,-4] in the direction y = -4x

I found out that b2 = [-4,-1] orthogonal to the line

Therefore,

rho(b1) = b1 - 4b2

= -4b1 - b2

Will the matrix be

|1 -4 |

|-4 -1|

Find the matrix of rotation, if the angle of rotation is 45 degrees, the axis of rotation points in the direction of [1,2,2] and if the rotation id counterclockwise. Also repeat the same problem, if the rotation is clockwise.

I started off saying that

I found an orthogonal vector to [1,2,2]

b1=[ -4,1,1]

b3= [1/(sqrt5), 1/(sqrt5), 1/(sqrt5)]

b2 = -b1 * b3

Am I on the right track?

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# Matrix in Rotation

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