Matrices

U

Identity matrix

the “1” of matrixes, multiplies to give the same matrix, 1 from top left to bottom right, can only be squares

rotation matrix 2d

how to find enlargement scale factor in a multiple transformation matrix

square root of the determinant

steps to find planes within each other

if the set of equations is multiples of each other

how to know when all planes meet at 1 pointe

equations are consistent

rotation about the x axis

rotation about the y axis

rotation about the z axis

how to find determinant of a 3×3 matrix

inverse of a 2×2 matrix

inverse of a 3×3 matrix

if the set of equations are inconsistent with no solutions and not multiples

prism

if the set of equations are inconsistent with infinite solutions and not multiples

sheaf

flowchart for finding geometric interpretation

if matrix is singular, form equations with 2 unknowns by elimination, then check if this can be solved

then see if any of the planes are parallel

no solutions and equations are multiples

at least 2 of the planes are parallel

what is an invariant point

a point that does not change due to the transformation

what is an invariant line

a line that maps to itself, even if points within it move

what type of transformation does this matrix represent

what does it mean if the det of a stretch is negative

theres also been a reflection

successive transformations matrix

second trans x first trans = total transformation

what does the determinant of a linear transformation mean

the area scale factor (for 2d)