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Unformatted text preview: 4-6 Matrix Equations
Consider the system of equations:
x1 2x1 + x2 +
2x2 3x2 x3
1 We can write this equation in matrix form, as follows:
1 let A = 0 2 −1
3 1 − 1 , X = 0 now our matrix equation is: x1 x2 , B = x3 1 1 1 AX = B • if A-1 exists
• we can do some algebra with our matrix equation
• much like solving ordinary linear equations:
AX = B
A-1AX = A-1B
IX = A-1B
X = A-1B (mult both sides on the left by A -1) Voila! We have solved our equation.
Bad news: we need to compute A-1 to do it this way!!!
Good news: once we have A-1, we can easily solve the
system for any B –– just multiply B on the left by A -1 !!! 4-6 p. 1 ...
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This note was uploaded on 12/11/2011 for the course MATH 1324 taught by Professor Staff during the Spring '11 term at Austin Community College.
- Spring '11