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A equals B A + B (Addition) c A scalar times a matrix A – B (subtraction)

Sec 3.4 Matrix Operations. A equals B A + B (Addition) c A scalar times a matrix A – B (subtraction). Sec 3.4 Matrix Operations. Quiz #1 on Online at 6:29pm-7:00pm Sec 3.1 + Sec 3.2. A=[1,2,1;3,8,7;2,7,9]. Sec 3.4 Matrix Operations. Column vector nx1

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A equals B A + B (Addition) c A scalar times a matrix A – B (subtraction)

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  1. Sec 3.4 Matrix Operations • A equals B • A + B (Addition) • c A scalar times a matrix • A – B (subtraction)

  2. Sec 3.4 Matrix Operations

  3. Quiz #1 on Online at 6:29pm-7:00pm Sec 3.1 + Sec 3.2 A=[1,2,1;3,8,7;2,7,9]

  4. Sec 3.4 Matrix Operations • Column vector nx1 • Row vector 1xn

  5. Sec 3.1 Introduction to Linear System Sec 3.2 Matrices and Gaussian Elemination Coefficient Matrix 3 x 3 Augmented Coefficient Matrix 3 x 4 Matrix Form Column vector 3x1

  6. The General Solution invector form The infinite solution set of the system is described by the equations: Consider the homog system: the reduced echelon form of the augmented matrix is: The general sol can be expressed in vector form: Leading variables: Free variables: The solution X is a linear combination of two vectors (2,1,1,0)^T and (3,-4,0,1)^T

  7. Sec 3.4 Matrix Operations Matrix Multiplication C = A * B mxnmxppxn

  8. Matrix Multiplication C = A * B mxnmxppxn j-thcolm j-thcolm of B i-th row i-th row of A

  9. Matrix Multiplication C = A * B mxnmxppxn

  10. Matrix Multiplication Let C = A * B

  11. Sec 3.4 Matrix Operations Matrix Algebra Commutative law of addition: Associative law of addition: Associative law of multiplication: Distributive laws:

  12. Sec 3.4 Matrix Operations Zero Matrix Identity Matrix

  13. Sec 3.4 Matrix Operations Matrix Algebra Not all of the rules of “ordinary” algebra carry over to matrix algebra Ordinary Algebra Matrix Algebra x x True x x

  14. Sec 3.4 Matrix Operations Use the matrix multiplication to show that if and are two solutions of the homogeneous system AX = 0 and and are real numbers, then is also a solution.

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