Lecture 6 Notes

# X c 5 3 solutions to homogeneous matrix equations ax 0

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Unformatted text preview: − x3 = 0 3 and 1 x1 = x3 3 5 x2 = − x3 3 Ax = 0 . 5 x2 + x3 = 0 3 and x3 can be whatever. 1 x1 = C 3 5 x2 = − C 3 x3 = C • Thus, the solution can be written as 1 ￿ . x = C −5 3 Solutions to homogeneous matrix equations Ax = 0 where 1 −2 1 A = 2 −4 2 −1 2 −1 • Example 2. Solve the equation Solutions to homogeneous matrix equations Ax = 0 where 1 −2 1 A = 2 −4 2 −1 2 −1 • Example 2. Solve the equation Solutions to homogeneous matrix equations Ax = 0 where 1 −2 1 A = 2 −4 2 −1 2 −1 1 −2 1 A ∼ 0 0 0 000 • Example 2. Solve the equation • Row reduction gives Solutions to homogeneous matrix equations Ax = 0 where 1 −2 1 A = 2 −4 2 −1 2 −1 1 −2 1 A ∼ 0 0 0 000 • Example 2. Solve the equation • Row reduction gives • so x1 − 2x2 + x3 = 0 and both x2 and x3 can be whatever. Solutions to homogeneous matrix equations Ax = 0 where 1 −2 1 A = 2 −4 2 −1 2 −1 1 −2 1 A ∼ 0 0 0 000 • Example 2. Solve the equation • Row reduction gives • so x1 − 2x2 + x3 = 0 and both x2 and x3 can be whatever. 2 −1 x = C1 1 + C2 0 0 1 Solutions to homogeneous matrix equations Ax = 0 where 1 −2 1 A = 2 −4 2 −1 2 −1 1 −2 1 A ∼ 0 0 0 000 • Example 2. Solve the equation • Row reduction gives • so x1 − 2x2 + x3 = 0 x2 and x3 can be whatever. 2 −1 x = C1 1 + C2 0 0 1 and both Solutions to homogeneous matrix equations Ax = 0 where 1 −2 1 A = 2 −4 2 −1 2 −1 1 −2 1 A ∼ 0 0 0 000 • Example 2. Solve the equation • Row reduction gives • so x1 − 2x2 + x3 = 0 x2 and x3 can be whatever. 2 −1 x = C1 1 + C2 0 0 1 and both Solutions to homogeneous matrix equations Ax = 0 where 1 −2 1 A = 2 −4 2 −1 2 −1 1 −2 1 A ∼ 0 0 0 000 • Example 2. Solve the equation • Row reduction gives • so x1 − 2x2 + x3 = 0 x2 and x3 can be whatever. 2 −1 x = C1 1 + C2 0 0 1 and both Solutions to homogeneous matrix equations Ax = 0 where 1 −2 1 A = 2 −4 2 −1 2 −1 1 −2 1 A ∼ 0 0 0 000 • Example 2. Solve the equation • Row reduction gives • so x1 − 2x2 + x3 = 0 x2 and x3 can be whatever. 2 −1 x = C1 1 + C2 0 0 1 and both Solutions to homogeneous matrix equations Ax = 0 where 1 −2 1 A = 2 −4 2 −1 2 −1 1 −2 1 A ∼ 0 0 0 000 • Example 2. Solve the equation • Row reduction gives • so x1 − 2x2 + x3 = 0 x2 and x3 can be whatever. 2 −1 x = C1 1 + C2 0 0 1 and both Solutions to homogeneous matrix equations Ax = 0 where 1 −2 1 A = 2 −4 2 −1 2 −1 1 −2 1 A ∼ 0 0 0 000 • Example 2. Solve the equation • Row reduction gives • so x1 − 2x2 + x3 = 0 x2 and x3 can be whatever. 2 −1 x = C1 1 + C2 0 0 1 and both Solutions to homogeneous matrix equations Ax = 0 where 1 −2 1 A = 2 −4 2 −1 2 −1 1 −2 1 A ∼ 0 0 0 000 • Example 2. Solve the equation • Row reduction gives • so x1 − 2x2 + x3 = 0 x2 and x3 can be whatever. 2 −1 x = C1 1 + C2 0 0 1 and both Solutions to homogeneous matrix equations Ax = 0 where 1 −2 1 A = 2 −4 2 −1 2 −1 1 −2 1 A ∼ 0 0 0 000 • Example 2. Solve the equation • Row reduction gives • so x1 − 2x2 + x3 = 0 x2 and x3 can be whatever. 2 −1 x = C1 1 + C2 0 0 1 and both Solutions to homogeneous matrix equations Ax = 0 where 1 −2 1 A = 2 −4 2 −1 2 −1 1 −2 1 A ∼ 0 0 0 000 • Example 2. Solve the equation • Row reduction gives • so x1 − 2x2 + x3 = 0 x2 and x3 can be whatever. 2 −1 x = C1 1 + C2 0 0 1 and both Solutions to homogeneous matrix equations Ax = 0 where 1 −2 1 A = 2 −4 2 −1 2 −1 1 −2 1 A ∼ 0 0 0 000 • Example 2. Solve the equation • Row reduction gives • so x1 − 2x2 + x3 = 0 x2 and x3 can be whatever. 2 −1 x = C1 1 + C2 0 0 1 and both Solutions to non-homogeneous matrix equations • Example 3. Solve the equation 1 A = 1 2 2 −1 1...
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## This note was uploaded on 02/12/2014 for the course MATH 256 taught by Professor Ericcytrynbaum during the Spring '13 term at The University of British Columbia.

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