Matrix

Matrix

Matrix (plural matrices) . a collection of numbers Matrix (plural matrices)  a collection of numbers arranged in a rectangle

Matrix (plural matrices) . a collection of numbers Matrix (plural matrices)  a collection of numbers arranged in a rectangle  sometimes generalized to mean anything arranged in an orderly pattern

We usually put brackets around matrices to show the numbers are grouped together. 3 −5 2 0 4 −9

The numbers in a matrix are arranged in rows and columns The numbers in a matrix are arranged in rows and columns. 3 −5 2 0 4 −9 has 2 rows and 3 columns.

We say 3 −5 2 0 4 −9 is a 2 x 3 matrix. The dimensions or size of the matrix are 2 x 3.

Find the dimensions of this matrix. 5 −2 4 −1 7 3 4 −3 1

Find the dimensions of this matrix. 5 −2 4 −1 7 3 4 −3 1 3 x 3

Find the dimensions of this matrix. 3 −1

Find the dimensions of this matrix. 3 −1 2 x 1

Find the dimensions of this matrix. 1 2 3 4 5 6 7 8 9 10

Find the dimensions of this matrix. 1 2 3 4 5 6 7 8 9 10 5 x 2

How many rows are in this matrix? −3 5 7 −3 5 7

How many rows are in this matrix? −3 5 7 −3 5 7 2

How many columns are in this matrix? 1 1 1 1 1 1

How many columns are in this matrix? 1 1 1 1 1 1 3

We can identify specific entries of a matrix by the row and column We can identify specific entries of a matrix by the row and column. For instance if 𝐴= 3 −5 2 4 −9 0 then 𝐴 31 =−9

𝐴= 3 −5 2 4 −9 0 Find 𝐴 32 Find 𝐴 21 Find 𝐴 12

𝐴= 3 −5 2 4 −9 0 Find 𝐴 32 = 0 Find 𝐴 21 = 2 Find 𝐴 12 = -5

𝐴 32 =8 𝐴 42 =0 𝐵 22 =1

If matrices are equal, then all their corresponding entries are equal.

If matrices are equal, then all their corresponding entries are equal

If matrices are equal, then all their corresponding entries are equal If matrices are equal, then all their corresponding entries are equal. 5 𝑥 3𝑧 20 = 𝑤 2𝑤 24 𝑦−3 w = 5 x = 2w = 25 = 10 20 = y – 3, so y = 23 3z = 24, so z = 8

x = -1.5 y = 0 z = 2 a = 6 b = 3 c = 2

Scalar Multiplication . A scalar is just a number.  Scalar Multiplication  A scalar is just a number.  You’re just taking a number times a matrix.

It’s a lot like the distributive property It’s a lot like the distributive property. Just multiply each entry by the scalar.

Adding and subtracting matrices

Adding and subtracting matrices Just add or subtract the corresponding entries.

Adding and subtracting matrices

Suppose 𝐴= 3 −5 −2 7 and 𝐵= 4 0 5 1 Find A + B A – B B – A

𝐴= 3 −5 −2 7 and 𝐵= 4 0 5 1 𝐴+𝐵= 7 −5 3 8

𝐴= 3 −5 −2 7 and 𝐵= 4 0 5 1 𝐴−𝐵= −1 −5 −7 6

𝐴= 3 −5 −2 7 and 𝐵= 4 0 5 1 B−𝐴= 1 5 7 −6

𝐴= 3 −5 −2 7 and 𝐵= 4 0 5 1 Find 3𝐴+2𝐵

𝐴= 3 −5 −2 7 and 𝐵= 4 0 5 1 Find 3𝐴+2𝐵 9 −15 −6 21 + 8 0 10 2 17 −15 4 23

It’s fairly easy to work with matrices on graphing calculators.

To use MATRIX mode on a graphing calculator, either . Find a key that To use MATRIX mode on a graphing calculator, either  Find a key that says MATRIX or  Press 2nd and the x-1 key

Once in MATRIX mode, choose EDIT, then choose the name of a matrix (like “A”).

You will first need to enter the number of rows and columns in your matrix. Hit ENTER after each. For instance, if 𝐴= 3 −5 −2 7 type 2 ENTER 2 ENTER

Then type each number in the matrix. . Go across the rows.  Then type each number in the matrix.  Go across the rows.  Hit ENTER after each.

Once you’re done entering the numbers, press 2nd and MODE (Quit) to go back to the main screen.

Now let’s enter 𝐵= 4 0 5 1

Once you have entered the matrices, you can go to MATRIX and “NAMES” to put the names of matrices on the screen.

Just press ENTER to get the final answer.

You could also do the subtraction problems this way.

𝐴= 3 −5 −2 7 and 𝐵= 4 0 5 1 Find 3𝐴+2𝐵

The calculator really doesn’t save much time with addition and subtraction, but it will be more useful when we do multiplication (which isn’t really common sense) and other operations with matrices.