Matrices

Question 1

How to solve for eigenvalues?

Answer 1

Solve the equation: det(M - λI) = 0.

Question 2

How to solve for eigenvectors?

Answer 2

Find eigenvalues first, then solve (M - λI)v = 0 by substituting for each eigenvalue λ. V is a random vector xyz

Question 3

What are the equations of a plane?

Answer 3

General form: Ax + By + Cz + D = 0, where A, B, C are coefficients and D is a constant. Parametric r = a + d1+ d2. vector dot product form too n.(r-a)=0

Question 4

sim eqns plane meaning of consistents vs inconsistent

Answer 4

Consistent: there is at least one solution to all 3.

Inconsistent, there is no solution

Question 5

what conidition must suffice for there to be a unique solution for planes

Answer 5

detA not equal 0

Question 6

condition for inconsistent

Answer 6

singular coefficient matrix detA=0

Question 7

formula for diagonalised matrices and explaination of variables

Answer 7

M=UDU^-1
M^n=UD^nU^-1

D-Diagnoalised matrix of eigen values
U eigen vector columns, must be in same order as corresponding eigenvalues in D

Question 8

How to find inverse of 2x2?

Answer 8

1/DetA multiplied by: swap leading diagonal, negative 1 the other diagonal