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Lesson 5

Lesson 5. Using matrices to organize data and to solve problems. Matrix. A matrix is a rectangular array of numbers. The number of rows and columns in a matrix gives the dimensions of the matrix. A matrix with r rows and c columns is a r x c matrix. Address of an element.

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Lesson 5

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  1. Lesson 5 Using matrices to organize data and to solve problems

  2. Matrix • A matrix is a rectangular array of numbers. The number of rows and columns in a matrix gives the dimensions of the matrix. • A matrix with r rows and c columns is a r x c matrix

  3. Address of an element • Each number in the matrix is an element, and has a unique address which tells its location in the matrix. • The address of an element is formed by the lower case letter of the matrix name, followed by its row number and column number in subscripts.

  4. Matrix addition • Matrices can be used to store data that would otherwise be presented in a table. • To add 2 matrices, A and B, of the same dimensions, add each element in the first matrix to the element that is in the same location in the second matrix

  5. Commutative property holds for matrix addition • A + B = B + A

  6. Creating and adding matices • Create 2 matrices from the following data: • Male Female • 9 10 11 12 9 10 11 12 • JV 82 54 8 0 91 46 39 5 • Vars 44 62 71 124 22 45 112 137 • None 50 93 85 43 86 95 30 66 • Find M+F

  7. Zero matrix- additive identity matrix • A matrix in which every element is zero is a zero matrix. • A zero matrix is formed when a matrix as added to its additive inverse matrix. • The elements in an additive inverse matrix are the opposite of every element in the original matrix.

  8. -A is additive inverse of A • A = 4 -15 -A = -4 15 • 9 -1 -9 1 • A = (-A) = 0 0 • 0 0

  9. Matrix subtraction • To subtract 2 matrices of the same dimensions, A-B, take the opposite, or additive inverse of B and add it to A., or subtract elements in matching locations

  10. Finding additive inverse matrix • Find additive inverse matrix of : • 10 -6.5 • 0 3 • -3 4 • Multiply by -1 -10 6.5 • 0 -3 • 3 -4

  11. subtraction • 3 16 -1 9 • -23 0 - -18 14 • + 1 -9 = 4 7 • 18 -14 -5 -14

  12. Solving a matrix equation • 3 7 + X = 5 9 • 9 1 2 -6 • X = 5 9 - 3 7 = 2 2 • 2 -6 9 1 -7 -7

  13. Solving for variables in matrices • Solve for a,b,c,and d: • a+12 2b = 18 -14 • 23 d a+c 3 • a+12 = 18 so a = 6 • 2b = -14 so b = -7 • 23 = a+c so 23 = 6+c, c = 17 • d=3

  14. Scalar multiplication • A scalar is a constant by which a matrix is multiplied. • To multiply matrix A by scalar n, multiply every element of A by n-(like the distributive property) • 4 2 1 = 4(2) 4(1) = 8 4 • -6 3.5 4(-6) 4(3.5) -24 14

  15. Lab 2- storing and recalling data in a matrix • Follow along on page 27: • Input matrix A • Press 2ndx-1 to get to the matrix menu • Go to EDIT, then select 1:A to open matrix menu • The calculator will ask you for the dimensions- enter # of rows first, then # of columns • press ENTER after each • Input matrix B • Follow same steps, but input into 2:B

  16. Recalling matrices • Calculate A x B • Press 2ndx-1 • Select 1:A • Press ENTER • Press x • Press 2nd x-1 • Select 2:B • Press ENTER • Press ENTER

  17. Using calculator • To find inverse of matrix A • Press 2nd x -1 • Select 1:A • Press ENTER • Press x-1 • Press ENTER

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