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9/11 More systems of equations: RREF etc Augmented matrix of a system Use Row operations To get Row echelon form to determine how many solutions Proceed to Reduced row echelon form to get solutions (if any) x + 2y = 1 3x + 4y = 2 x y rhs 2 1 3 4 2. Common #2 Find RREF - PowerPoint PPT Presentation
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9/11 More systems of equations: RREF etc
Augmented matrix of a systemUse Row operationsTo get Row echelon form to determine how many solutionsProceed to Reduced row echelon form to get solutions (if any)
x + 2y = 13x + 4y = 2
x y rhs1 2 13 4 2
Common #2 Find RREF
-5 -3/2 2-5 -3/2 22 ½ 0
Mixture problems: give names to the various outputs andwrite the equations they must satisfy. Solve the system.
Common #3 3 equations in three variables
x y z rhs 1 1 1 234 1 -1 -1 0 25 35 56 8637
Consistent means:
Common #4 Find b so that the system is consistent
t – r = b-2t + r = 7 t – r = -4
Traffic flow problem: #
#7 find a so that the system does not have a unique soln
-2z + 2x + v = -2-2z +2v=-2az + x + 2v =2
#8 Find k so that there is either no solution or an infiniteNumber of solutions to
Matrix operations: The idea traces back to mid 1800’s
Replace a system of equations with a single matrix equation
x + y = 1x - y = 2
Stock portfolios Example of matrix multiplication
Bob Tom and Jane stock holdings
Stock IBM GE Toyota TI Stock Price Bob 20 30 14 2 IBM 30Tom 10 40 80 10 Ge 100Jane 50 21 10 24 Toy 75 TI 45
Portfolio matrix * price vector = portfolio value vector