MATH 152 midterm2 things

Rotation matrix

cos -sin

sin cos

Projection Formula

(xv)/(mag(V)²) * v

Projection Matrix

project each basis (column of identity matrix) separately)

V1² V1V2
V1V2 V2²

all divided by mag(V)²

Reflection Matrix

Projection Matrix plus…

-1 0

0 -1

them multiplied by 2

= 2[projMatrix] - x

Probabilities and Random walks

[Transition][Variables]

[Coefficients][Variables] of equations

(A+B)^T

A^T + B^T

(AB)^T or (AB)^-1

B^-1 * A^-1 or T

reverse the order

Determinant of a Diagonal Matrix

product of the diagonal

det(A^T)

det(A)

det(A^-1)

1/det(A)

det(AB)

det(A)det(B)

Det: Swap two rows

-1

Multiply row by scalar

*S

Add row to another

No Effect on Determinant

Opposite diagonal swaps: / → \

floor(n/2) swaps needed

A is INVERTIBLE when

det(A) ≠ 0

RREF(A) = Identity