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Add, Subtract, and Multiply Matrices

Add, Subtract, and Multiply Matrices. Matrix. A. A matrix M is an array of cell entries ( m row,column ) that have rectangular dimensions ( Rows x Columns ). Example:. a row,column. 4. 3. A. 15 x. 3x4. Dimensions:. Scalar Multiplication.

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Add, Subtract, and Multiply Matrices

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  1. Add, Subtract, and Multiply Matrices

  2. Matrix A A matrixM is an array of cell entries (mrow,column) that have rectangulardimensions (Rows x Columns). Example: arow,column 4 3 A 15x 3x4 Dimensions:

  3. Scalar Multiplication Every entry in the matrix is multiplied by the number outside the matrix (scalar). Example:

  4. Matrix Addition/Subtraction IF the matrices have the same dimensions, add or subtract correspondingcell entries. Examples: b+h

  5. Matrix Addition/Subtraction Perform the indicated operation: The matrices MUST have the same dimensions!

  6. Matrix Multiplication 1Multiply the elements of each row of the first matrix by the elements of each column in the second matrix. 2Add the products. 3The answer goes into arow of 1st, column of 2nd. 3x2 2x3 a1,2 a1,1 1 a2,2 a2,1 2 1 2 15 16 2x2 20 27

  7. Matrix Multiplication Can we multiply these… 5x1 2x3 2x2 3x4 ? No No 3x2 # of columns in 1st MUST be the same as # of rows in 2nd! 1x3 Yes

  8. Matrix Multiplication with a Context Cars Trucks Wheels Seats Gas Tanks Bull’s Eye Order Cars JC Nickels Department Store Order Trucks Wheels Gas Tanks Seats Bull’s Eye Total Order JC Nickels Department Store Total Order

  9. Matrices and the Calculator Follow the link below for instructions: http://www.cpm.org/pdfs/stuRes/A2C/chapter_07/7.3.3A.pdf

  10. Order in Matrix Multiplication Matters OR

  11. Matrix Multiplication The dimensions of a product of matrices are the # of rows of the first matrix by the # of columns of the second matrix. 3x3 3x3 3x3 3 3 3 3 (a) 1x3 3x3 3 1 1x3 3 1 (b) (c) 2x2 2x2 2x2 2 2 2 2 3x3 3 3x1 3x1 1 3 1 In order to multiply matrices, the # of columns in 1st matrix MUST be the same as # of rows in 2nd Matrix. (d)

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