X c 5 3 solutions to homogeneous matrix equations ax 0

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online