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NOTES 3.2

NOTES 3.2. TSW Identify matrix terminology Add Matrices Subtract Matrices Enter matrix in a calculator. A matrix is described by its dimensions: rows X columns. Notes 3.2 Matrices. one. one. equal. Matrices are used to organize data and solve systems of equations. zero. element.

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NOTES 3.2

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  1. NOTES 3.2 • TSW • Identify matrix terminology • Add Matrices • Subtract Matrices • Enter matrix in a calculator

  2. A matrix is described by its dimensions: rows X columns Notes 3.2 Matrices one one equal Matrices are used to organize data and solve systems of equations. zero element dimensions corresponding A row matrix has _____ row. A column matrix has _____ column A square matrix has ________ number of rows and columns A zero matrix has each ___________ as a _________ Equal matrices have the same __________ and each element of one matrix is equal to the ____________element of the other matrix.

  3. A matrix is usually named using a capital letter. element The dimensions of matrix A are ____ X ____ 2 3 4 9 dimensions Each value in a matrix is called an ___________ Find element A12 = ______ Find element A23 = ______ Matrices can only be added or subtracted if they have the same _______________

  4. Scalar Multiplication and Addition Teacher reminder: Show how to enter a matrix in TI83): DNE

  5. Solve for x and y x+3y = -13 y = -3 3x+y = 1 2x+(-3)=5 Solve the system! x = 4

  6. Solve for Matrix A

  7. 1 3 3 2 Dimensions……. A = ___x___ B=___x___ AB = ___x___ 1 2 Multiply matrices: Find AB Also mult on calc.!

  8. Rule for multiplying matrices Commutative property AB=BA If the number of columns in the first matrix is not equal to the number of rows in the 2nd matrix, then the product of the two matrices is not defined, or “Does not Exist” or “DNE” This property is not always true for matrices. If A= 2x3 and B= 3x4 You can find AB …..but not BA

  9. Solve for w and z Now solve linear equations! This represents 4 equations! Row 1 col 1: -2 Row 1 col 2: -23 (-3)(4)+(-2)(-5) = -2 (-3)(w)+(-2)(1) = -23 w = 7 Row 2 col 2: 6 Row 2 col 1: z (0)(4)+(6)(-5)= z (0)(w)+(6)(1) = 6 Z = -30

  10. Write the equations and solve the system. -3x+2y = 7 -5x+6y = 17 9x-6y = -21 -5x+6y = 17

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