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MATRICES

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MATRICES

Danny Nguyen

Marissa Lally

Clauberte Louis

HOW TO'S:

ADD, SUBTRACT, AND MULTIPLY MATRICES.

- The dimensions of a matrix refer to the number of rows and columns of a given matrix.
# of rows x # of columns

- The subtraction of matrices is only allowed if matrices are the SAMEsize!!
- If the matrix doesn't have the same # of rows and columns you cannot subtract them.

-3

5

ERROR!

4 -7

- You CANNOT subtract 1 x 2 matrix and a 2 x 1 matrix!
- They are NOT the same size
- You can't just flip the second matrix to make it the same either!

WHAT?!

2 -5 1

7 10 -1

1 2 3

4 5 6

1-22-(-5) 3-1

4-75-106-(-1)

-1 7 2

-3 -5 7

0 1 2 6 5 4

9 8 7 3 4 5

HOW TO SOLVE?

Both or more matrices must have the same dimensions to be able to add, if not, the operation cannot be done.

(0 + 6) (1 + 5) (2 + 4)

(9 + 3) (8 + 4) (7 + 5)

6 6 6

12 12 12

ADDING MATRICES

For example, you cannot add a 2x3 matrix with a 3x2 matrix.

0 2 4 5 7

5 4 5 2 1

ERROR!

Multiplying matrices

(property)

To multiply an m×n matrix by an n×p matrix, the ns must be the same, and the result is an m×p matrix.

Associative property:

A (BC) = (AB) C

Example:

4 x (3 x 2) = 24 or (2 x 4) x 3 = 24

Left distributive property:

A (B + C) = AB+ AC

Example:

2 x (3 + 4) = 2×3 + 2×4

Associative property (scalar):

C(AB)=(cA)B=A(cB)

Example:

3 x (2 x 5) = (3 x 2) x 5 = 2 x (3 x 5)

Right distributive property:

(A + B) C = AC+ BC

Example:

(2+3) x4 = 2x 4 +3 x 4

Multiplying matrices

( scalars)

Explanation: If you are multiply a matrix by a scalar you have to multiply each entry in the matrix by the scalar.

Example:

We call the number ("2" in this case) a scalar, so this is called

"scalar multiplication".

calculations:

Multiplying matrices

(dot product)

Explanation: When multiply a 1 × n matrix by an n × 1 matrix, you want to know the first row is a single row and the second is a single column. You want to: name the rows and then the column. Then the product of the row and column is formed. (1 × 1 matrix)

you want to do 1st row by 1st column.

( 1, 2, 3) • (7, 9, 11) = 1×7 + 2×9 + 3×11 = 58

you want to do 1st row by 2nd column

(1, 2, 3) • (8, 10, 12) = 1×8 + 2×10 + 3×12 = 64

DONE!!