Matrices

Question 1

Matrix Multiplication

Answer 1

Can be different sizes, but the column of A and row of B must be the same. The new size is the outside dimensions. To multiply, split first matrix into rows, split second matrix into columns, and find cross product.

Question 2

Matrix Inverses

Answer 2

Only available in square matrices. A * A^-1 = Identity Matrix

Question 3

Solving Matrix Equations

Answer 3

Ax = b, x = A^-1 * b

Question 4

Co-Factor Equation

Answer 4

C(ij) = (-1)^i+j * M(ij)

Question 5

Finding Minors

Answer 5

At a particular element’s row and column, find the determinant of the remaining values.

Question 6

Determinant of any n x n matrix

Answer 6

Det = sum of (element * Co-Factor) across a row or down a column. Same across any row or down any column, pick the one with most 0’s.

Question 7

Triangular Matrix

Answer 7

Either has zeros below the diagonal, or above the diagonal. In this case, the determinant is the product of values down the diagonal

Question 8

Changes to determinant

Answer 8

1. Exchanging rows multiplies the determinant by -1
2. Multiplying a row by a constant changes the determinant by that constant
3. Adding a multiple of a row to another row doesn’t change the determinant

Question 9

Cross Product Matrix

Answer 9

For two vectors, the cross product is equal to the determinant of remaining values. Equation = det(i) - det(j) + det(k)

Question 10

Cross Product for orthogonal vectors

Answer 10

u * (u x v)

Question 11

Area of Triangle from two vectors

Answer 11

0.5 * Magnitude of Cross Product