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4.1, 2, 3 Perform Basic Matrix Operations

4.1, 2, 3 Perform Basic Matrix Operations. By the end you should: 1. add and subtract matrices 2. multiply by a scalar 3. solve a matrix equation 4. multiply matrices. The Matrix. Vocab: Matrix: a rectangular arrangement of numbers in rows and columns

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4.1, 2, 3 Perform Basic Matrix Operations

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  1. 4.1, 2, 3 Perform Basic Matrix Operations By the end you should: 1. add and subtract matrices 2. multiply by a scalar 3. solve a matrix equation 4. multiply matrices The Matrix Vocab: Matrix: a rectangular arrangement of numbers in rows and columns Dimensions: matrix with m rows and n columns denoted m x n read "m by n" Elements: numbers inside the matrix Equal Matrix: dimensions are the same; elements in corresponding positions are equal; they look the same

  2. dimensions = ______________ name the element in the 1st row 2nd column _______ dimensions = ______________ name the element in the 3rd row 3rd column _______ dimensions = ______________ name the element in the 1st row 1st column _______

  3. Your Turn: 1. 2.

  4. Adding and Subtracting Matrices you can ONLY do this is they have the SAME dimensions you will end up with ONE matrix ADD SUB

  5. Your Turn: 1. 2.

  6. Scalar Multiplication scalar is a number it uses the distributive property

  7. Properties of Matrix Operations A, B, and C are matrices with the same dimensions, and k is a scalar • Associative Property of Addition (A + B) + C = A + (B + C) • Commutative Property of Addition A + B = B + A • Distributive Property of Addition k(A + B) = kA + kB • Distributive Property of Subtraction k(A - B) = kA - kB

  8. Solve a Matrix Equation Solve for x and y by breaking it down use what you know to be true CHECK your answers!

  9. Your Turn: 1. 2.

  10. Solve a Matrix Equation Mary asked both the male and female players on two Basketball Teams what color the new team uniforms should be: red, blue, or green. She recorded the results in two matrices. Find the totals for the teams.

  11. Addition of matrices and multiplication of a matrix by a scalar

  12. Exit Card 4.1: Name: _____________________________

  13. Brain Teaser: Camp Pineveiw's cook, Margaret Johnson, was just about to begin preparing the picnic lunch for all the campers. She already knew she needed to fill 55 bowls of the same size and capacity with the same amount of food. When she was done, she decided to read the guidelines for the picnic, just out of curiosity. The guidelines said:1. Every camper gets their own bowl of soup.2. Every two campers will get one bowl of spaghetti to share.3. Every three campers will get one bowl of salad to share.4. All campers are required to have their own helping of salad, spaghetti, and soup.After some rapid calculations, Margaret was able to figure out how many campers were going to the picnic. Can you? Hint If there were only six campers, there would be six bowls of soup, three bowls of spaghetti, and two bowls of salad

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