Unit 7-Systems and Matrices

Question 1

Matrix

Answer 1

Rectangular array of numbers in rows and columns

Question 2

Dimensions/order are written as…

Answer 2

Rows X Columns

Question 3

Elements/entries

Answer 3

numbers inside
atinyij, ith row and jth column

Question 4

Square Matrix

Answer 4

When I=J

Question 5

Two matrices are equal when…

Answer 5

they have the same dimensions and corresponding elements are equal

Question 6

Add/subtract matrices

Answer 6

Add/subtract corresponding parts

Question 7

Additive Inverse

Answer 7

Multiply matrix A by -1

Question 8

Matrix Multiplication

Answer 8

Take row of first matrix and multiply it by columns of the second matrix.
Each column, multiplied numbers are added
Can only multiply two matrices if their inner dimensions are the same

Question 9

Identity Matrix

Answer 9

When multiplying identity Matrix with matrix, there is no impact to the OG matrix
Identity matrices are always square
Identity matrix have a diagonal of 1s and 0s everywhere else

Question 10

Singular Matrix

Answer 10

When a matrix has no inverse

Question 11

Determinant of a 2X2 matrix

Answer 11

ad-bc

Question 12

Inverse of a 2X2 Matrix

Answer 12

1/determinant * [ d -b (on top) -c a (on bottom]

Question 13

Determinant of 3X3 Matrix

Answer 13

Switch +, -, + of the top row. Do determinant thingy for a 2X2 but crossing any numbers that are in the same row and column of that top row number.
1.1 (ad-bc) -2.1 (ad-bc) + 3.1 (ad-bc)

Question 14

Finding Areas of Triangles

Answer 14

+/- 0.5 * [ x1 y1 1 (top row) x2 y2 1 (middle row) x3 y3 1 (bottom row)]
xs and ys are coordinate points

Question 15

Transpose Matrix

Answer 15

Switch rows and columns

Question 16

Row Echelon Form

Answer 16

Convert matrix so it has 1s in the main diagonal and 0s below this main diagonal

Question 17

Reduced Row Echelon Form

Answer 17

Same as Row Echelon Form except there are 0s above the main diagonal too

Question 18

Finding 2X2 Inverse using Row Operations

Answer 18

Write matrix and after put a line and write the identity matrix. Change matrix into identity matrix and the numbers on the other side is the inverse

Question 19

Partial Fraction Decomposition

Answer 19

Factor Denominator
Put A and B as the numerators
Multiply fractions with opposite denominators
Write two equations; numerator equation and denominator equation
Solve for A and B using matricies

Question 20

Encrypting

Answer 20

Put letters in a # X 2 matrix
Multiply by encoding matrix
Write product of the matrices as a string of numbers

Question 21

Decoding

Answer 21

Write decoding into a # X 2 matrix
Multiply by inverse to the coding matrix
Match product of the matrices with letters
Multiply coded matrix by inverse of coding matrix = Decoded matrix