063 19 288888 067676767 045673891983637 Matrix September 14 2017 Lets watch a short video httpswwwkhanacademyorgmathprecalculusprecalcmatricesintrotomatricesvintroductiontothematrix ID: 915129
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Slide1
Bell work
What is the fraction of the following decimals?
0.63
1.9
2.88888.....
0.67676767.....
0.45673891983637.....
Slide2Matrix
September 14, 2017
Slide3Let's watch a short video
https://www.khanacademy.org/math/precalculus/precalc-matrices/intro-to-matrices/v/introduction-to-the-matrix
Slide4Matrices
A matrix is a rectangular array of numbers arranged in rows and columns. The dimensions of a matrix are written as
Rows x columns
Slide5examples
This is a 2 x 3 matrix
2 down, 3 across
This is a 3 x 2 matrix
3 down, 2 across
Slide6Naming matrices
A capital letter is used to name a matrix.
This is Matrix A.
Each individual entry is name by its position in the matrix.
a23 is row 2, column 3
Slide7Try to locate
a13
a24
a33
Slide8Special matrices
A
square matrix
have the same number of rows as columns.
1 x 1
2 x 2
3 x 3
Etc.
Slide9Special matrices
A matrix with all zeros is called a
zero matrix
.
Slide10Special matrices
An
identity matrix
is a square matrix with 1s in the square location (a11, a22, a33, etc.) and zeros in every other location. Forms a diagonal of 1s.
Named with a capital I.
Slide11Equal matrices
Two matrices are equal if:
They have the same dimensions.
The corresponding entries are equal.
Slide12Using equal matrices
Equal matrices can be use to solve for variables.
Slide13Bell work: Which matrices are equal?
Slide14matrices
September 15, 2017
Slide15Adding matrices
Can only add matrices if they have the same dimensions.
To add, just add the corresponding entries and place the sum in the corresponding position in the matrix.
Slide16Practice
Try these
Slide17Subtracting matrices
Can only subtract matrices if they have the same dimensions.
To subtract, just subtract the corresponding entries and place the difference in the corresponding position in the matrix.
Slide18practice
Try these.
Slide19Multiplying matrices by a scalar
Multiply the scalar (number outside the matrix) by every number inside the matrix.
Slide20Practice
Try these
Slide21Bell work
Subtract the following matrices.
Slide22matrices
September 18, 2017
Slide23Multiplying 2 matrices together
Start with Row 1 of the first matrix and Column 1 of the second matrix.
(1•7) + (2•9) + (3•11) = 58
Next with Row 1 of the first matrix and Column 2 of the second matrix.
(1•8) + (2•10) + (3•12) = 64
Next with Row 2 of the first matrix and Column 1 of the second matrix.
(4•7) + (5•9) + (6•11) = 139
Lastly, Row 2 of first matrix and Column 2 of the second matrix.
(4•8) + (5•10) + (6•12) = 154
Slide24What do you notice...
...about the dimensions of the matrices when you multiply two matrices together?
Do you think it always has to be this way?
Slide25To multiply Matrices
The number of columns of the first matrix
HAS
to match the number or rows in the second matrix.
Dimensions of the new matrix ill be the number of rows in the first by the number of columns in the second.
Slide26Practice
Try this one.
First: what will the dimensions of the product be?
https://www.youtube.com/watch?v=BGbiHdKHG7o
Slide27Bell work
Add the following matrices.
Slide28Exponent Laws
September 19, 2017