This preview shows page 1. Sign up to view the full content.
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 nonhomogeneous 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.
 Spring '13
 EricCytrynbaum
 Differential Equations, Geometry, Equations

Click to edit the document details