matrices and linear transformations notes

Ch 6&7 Core Pure

what does this matrix represent & what are its invariant points/ is there an invariant line?

reflection in the y-axis , invariant line of x=0

what does this matrix represent & what are its invariant points/ is there an invariant line?

reflection in the x-axis, invariant line of y=0

what does this matrix represent & what are its invariant points/ is there an invariant line?

reflection in the line y=x, invariant line of y=x

what does this matrix represent & what are its invariant points/ is there an invariant line?

reflection in y=-x, invariant line of y=-x

what does this matrix represent & what are its invariant points/ is there an invariant line?

a rotation angle θ anticlockwise about the origin, invariant point (0,0)

what does this matrix represent & what are its invariant points/ is there an invariant line? what does it represent when a=b?

stretch of scale factor a parallel to the x-axis, and scale factor b parallel to the y-axis (where a=b it is an enlargement scale factor a)

what does this matrix represent & what are its invariant points/ is there an invariant line?

reflection in the plane x=0

what does this matrix represent & what are its invariant points/ is there an invariant line?

reflection in the plane y=0

what does this matrix represent & what are its invariant points/ is there an invariant line?

reflection in the plane z=0

what does this matrix represent & what are its invariant points/ is there an invariant line?

a rotation , angle θ, anticlockwise around the x-axis

what does this matrix represent & what are its invariant points/ is there an invariant line?

a rotation , angle θ, anticlockwise around the y-axis

what does this matrix represent & what are its invariant points/ is there an invariant line?

a rotation , angle θ, anticlockwise around the z-axis

what does the transformation A^-1 describe?

the reverse of the transformation represented by matrix A