Level 335
Level 337

#### 62 words 0 ignored

Ready to learn
Ready to review

## Ignore words

Check the boxes below to ignore/unignore words, then click save at the bottom. Ignored words will never appear in any learning session.

**Ignore?**

matrix

a rectangular array of elements (or entries) set out by rows and columns

Column

vertical linear array of numbers

row

a hortizontal array of numbers side by side

zero matrix

matrix containing zeros

diagonal matrix

has zeros in all positions other than the leading diagonal which contains numbers other than zero.

elements

What are the objects in a set called?

matrices

plural of matrix

(m X n) matrix

A matrix with m rows and n columns

3B

B + B + B

Subtraction of matrix

subtracting corresponding elements

adding and subtracting of matrices

only on matrices of the same order

multiplication by a scalar (number)

each element is multiplied by the scalar

equality of matrices

matrices are equal if they are of the same order and all corresponding elements are equal

identity matrix

diagonal matrix with ones in the leading diagonal and zeros in the other positions.

square matrix

the same number of elements in the rows and columns.

A X B exists and order is m X p

A = m X n and B = n X p, then A X B

AI = IA

A is a square matrix and I is the identity matrix

A^-1

inverse matrix

AX = B

X = A^-1X B

XA = B

X = BA^-1

entries

the numbers in a matrix

dimensions, example

2 by 3

rows

what does the 2 represent in 2x3

columns

what does the 3 represent in 2x3

row matrix

a matrix has only 1 row

column matrix

a matrix has only 1 column

how are two matrices equal?

if their dimensions are the same and the entries in corresponding positions are equal

the dimensions have to be the same

what must occur in order for matrices to be able to be added and subtracted?

what is the communitive property?

axb is the same as bxa

No

are matrices communitive?

what is the associative property?

a(bc) is the same as (ab)c

Yes

are matrices associative?

det A or |A|

how is a determinant denoted by?

keep the area positive

when finding the area of the triangle, what do you always do?

5+0=5 or 5x1=5

what is the identity property?

5+ (-5)= 0

what is the inverse property?

multiply by 1 0

in a 2x2 matrix, how do you get the multiplicative identity?

multiply by 1 0 0

in a 3x3 matrix, how do you get the multiplicative identity?

addition and substraction

add or subtract corresponding entries- cant add/ subtract with unequal dimensions

equal matrices

-dimensions are the same

properties of matrix addition

commutative property of matrix addition

matrix multiplication

-can be multiplied if the # of A columns = # of B rows

does not hold true

commutative property of matrix multiplication

Additive Identity

The additive identity is 0. a + 0 = 0 + a = a

additive inverse

the opposite of a number

Multiplicative Identity

A * 1 = A

multiplicative inverse

reciprocal of a number

determinants

2x2 (cross multiply and subtract)

additive identity matrices

multiply the matrix by a matrix with all zeros

additive inverse matrices

multiply the matrix by a matrix by the same matrix except all entries are negated

multiplicative identity matrices

only for square matrices- (nxn) with a diagonal of 1s from left to right

multiplicative inverse matrices

1/det [d -b -c a]

solving matrix equa

[A] X = [B] (multiply A(-1) times B = X)

solving systems with matrices

8x + 5y = 2

Transformation

a movement on the cartesian plane

[1 0, 0 -1]

reflective about the x-axis transformation

[-1 0, 0 1]

reflective about the y-axis transformation

Dilation

a transformation that changes the size of an object, but not the shape

90* rotation

switch the x and y values and negate the x values [0 -1, 1 0]

180* rotation

negate all values -1[ ]

270* rotation

switch the x and y values and negate the y values [0 1, -1 0]

360*

same [1 0, 0 1]