4.1, 4.2, 4.3 matrix notes...
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4.1, 4.2, 4.3 MATRIX NOTES 201516.notebook May 25, 2016
4.1, 4.2, and 4.3 MatricesI can: add, subtract, and multiply matrices and solve matrix equations. I can compute with matrices on my calculator using Alpha Zoom.
BRING YOUR BOOKS TOMORROW PLS
4.1, 4.2, 4.3 MATRIX NOTES 201516.notebook May 25, 2016
ON FRIDAY,
YOU WILL TAKE OUT YOUR PACKET AND TRANSFER 1015 RANDOMLY CHOSEN ANSWERS WITH WORK
AND TRANSFER TO A SHEET TO BE GRADED FOR SUMMATIVE
4.1 Organizing Data into Matrices
A matrix (plural: matrices) is a rectangulararray of numbers written within brackets.
You represent a matrix with a capital letter, and classify it by its dimensions.
4.1, 4.2, 4.3 MATRIX NOTES 201516.notebook May 25, 2016
The number of horizontal rows and vertical columns determine the dimensions of a matrix.
A = 2 3 4 6 7 0
3 columns-->2 rows
<--<--
-->-->
Matrix A is a 2 x 3 matrix.
Write the dimensions of each matrix.
a. 4 6 5 2 -3 -7 1 0 9
c. -4 3 -3
b. 120.5
EX 1
4.1, 4.2, 4.3 MATRIX NOTES 201516.notebook May 25, 2016
Energy is often measured by British thermal units. Write a matrix to represent the databelow. Estimate the values from the graph.
China
Russia
U.S.
Annual Energy Production and Consumption
0 20 40 60 80 100 Let each row represent a country and each columnrepresent production or consumption levels.
China Russia U. S.
Production Consumption
red = prod.blue = consumption
Ex 2
WS 4.1
[ ] =[ ]2/3a9b
2c1/4d
2458
3 1/336
be a thinker....
a = 36b = 6 4/9c = 5/3d = 144
ex 3
4.1, 4.2, 4.3 MATRIX NOTES 201516.notebook May 25, 2016
4.2 Adding and Subtracting Matrices
You perform matrix addition (or subtraction) on matrices with equal dimensions by adding (or subtracting) the corresponding elements (elements in the same position in each matrix).
Find each sum. ex 4.
Just add corresponding elements
4.1, 4.2, 4.3 MATRIX NOTES 201516.notebook May 25, 2016
Find the difference. Ex. 5 Just subtract corresponding elements
a.
b. 2 5 8 3 8 1.5 7 11 2.5 7
Finding Unknown Matrix Elements
Solve the equation
Equal Matrices are matrices with the same dimensions and equal corresponding elements.
Ex. 6
4.1, 4.2, 4.3 MATRIX NOTES 201516.notebook May 25, 2016
4.3 Matrix Multiplication
The number 3 is called a scalar, therefore this method of multiplication of matrices is called scalar multiplication.
You can multiply a matrix by a real number :
Find 3A.
ex 7
I CAN: add and subtract matrices with scalars and multiply matrices
Using Scalar ProductsFind the difference 5A 3B for
and
ex 8
4.1, 4.2, 4.3 MATRIX NOTES 201516.notebook May 25, 2016
Solving Matrix Equations with Scalars
Check?
ex 9
Multiplying Matrices
Multiply a11 and b11. Then multiply a12 and b21. Add the products.
The result is the element in the first row and first column.
Find the product
Multiply a11 and b12. Then multiply a12 and b22. Add the products.
The result is the element in the first row and second column.
Multiply a21 and b11. Then multiply a22 and b12. Add the products.
The result is the element in the second row and first column.
Multiply a21 and b12. Then multiply a22 and b22. Add the products.
The result is the element in the second row and second column.
ex 10
4.1, 4.2, 4.3 MATRIX NOTES 201516.notebook May 25, 2016
Multiplying Matrices
Find the product
ex 10
use Alpha Zoom