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Matrix Algebra

Matrix Algebra . Section 7.2. Review of order of matrices. Order is determined by: (# of rows) x (# of columns). 2 rows, 3 columns. Equality of Matrices. A = B Two Matrices A and B are equal if and only if both of the following are true A and B have the same order m x n

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Matrix Algebra

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  1. Matrix Algebra Section 7.2

  2. Review of order of matrices • Order is determined by: • (# of rows) x (# of columns) 2 rows, 3 columns

  3. Equality of Matrices • A = B • Two Matrices A and B are equal if and only if both of the following are true • A and B have the same order m x n • Every pair of corresponding elements are equal

  4. Given thatsolve for x and y x² = 25 x = 5, -5 2y + 3 = 25 2y = 22 y = 11

  5. Solve for each variable

  6. Matrix Addition and Subtraction • If A is an m x n matrix and B is an m x n, then you may add or subtract the corresponding elements in matrix A and matrix B.When adding or subtracting matrices, their orders must be the same.To add and subtract matrices, simply add or subtract each corresponding element.

  7. Find A + B A + B = Find A – B A – B =

  8. Multiplying by a Scalar • Order does not matter • Simply multiply each element in the matrix by the number (scalar) out front

  9. Multiply a Matrix by a scalar Find 2A Find -2B + A

  10. Multiply Matrices • The number of columns in the first matrix must be equal to the number of rows in the second matrix. • You can multiply a 2 x 3 matrix by a 3 x 5 matrix • You can NOT multiply a 2 x 3 matrix by a 2 x 3 matrix

  11. Find AB Order of matrix A is 2 x 2 Order of matrix B is 1 x 2 (2 x 2)(1 x 2) We CAN’T find AB Find BA (1 x 2)(2 x 2) CAN Multiply Resulting Matrix is 1 x 2

  12. BA = 5(2) + 7(-1) = 10 – 7 = 3 5(3) + 7(4) = 15 + 28 = 43 BA =

  13. Find AB

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