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Unformatted text preview: Ax = b 3
−2
1 and where 2
b = 0 .
2 Solutions to nonhomogeneous matrix equations
• Example 3. Solve the equation 1
A = 1
2 • Row reduction gives 2
−1
1 Ax = b 3
−2
1 10
0 1
00 and where 2
b = 0 .
2 −1/3 2/3
5/3 2/3
0 0 Solutions to nonhomogeneous matrix equations
• Example 3. Solve the equation 1
A = 1
2 • Row reduction gives • so 2
−1
1 Ax = b 3
−2
1 10
0 1
00 and where 2
b = 0 .
2 −1/3 2/3
5/3 2/3
0 0 1
2
5
2
x1 − x3 = and x2 + x3 =
3
3
3
3 and x3 can be whatever. Solutions to nonhomogeneous matrix equations
Ax = b .
5
2
x2 + x3 =
3
3 • Example 3. Solve the equation
• so 1
2
x1 − x3 = and
3
3 and x3 can be whatever. Solutions to nonhomogeneous matrix equations
Ax = b .
5
2
x2 + x3 =
3
3 • Example 3. Solve the equation 1
• so x1 − x3 =
3
1
x1 = x3 +
3 2
and
3
2
3 and x3 can be whatever. Solutions to nonhomogeneous matrix equations
Ax = b .
5
2
x2 + x3 = and x3 can be whatever.
3
3
5
2
x2 = − x3 +
3
3 • Example 3. Solve the equation 1
• so x1 − x3 =
3
1
x1 = x3 +
3 2
and
3
2
3 Solutions to nonhomogeneous matrix equations
Ax = b .
5
2
x2 + x3 = and x3 can be whatever.
3
3
5
2
x2 = − x3 +
3
3 • Example 3. Solve the equation 1
• so x1 − x3 =
3
1
x1 = x3 +
3 2
and
3
2
3 1
2/3
C −5 + 2/3
x=
3
3
0 Solutions to nonhomogeneous matrix equations
Ax = b .
5
2
x2 + x3 = and x3 can be whatever.
3
3
5
2
x2 = − x3 +
3
3 • Example 3. Solve the equation 1
• so x1 − x3 =
3
1
x1 = x3 +
3 2
and
3
2
3 2/3
1
x = C −5 + 2/3
0
3 Solutions to nonhomogeneous matrix equations
Ax = b .
5
2
x2 + x3 = and x3 can be whatever.
3
3
5
2
x2 = − x3 +
3
3 • Example 3. Solve the equation 1
• so x1 − x3 =
3
1
x1 = x3 +
3 2
and
3
2
3 2/3
1
x = C −5 + 2/3
0
3 the general solution to
the homogeneous
problem Solutions to nonhomogeneous matrix equations
Ax = b .
5
2
x2 + x3 = and x3 can be whatever.
3
3
5
2
x2 = − x3 +
3
3 • Example 3. Solve the equation 1
• so x1 − x3 =
3
1
x1 = x3 +
3 2
and
3
2
3 2/3
1
x = C −5 + 2/3
0
3 the general solution to
the homogeneous
problem one particular solution
to nonhomogeneous
problem Solutions to nonhomogeneous matrix equations
Ax = b .
5
2
x2 + x3 = and x3 can be whatever.
3
3
5
2
x2 = − x3 +
3
3 • Example 3. Solve the equation 1
• so x1 − x3 =
3
1
x1 = x3 +
3 2
and
3
2
3 2/3
1
x = C −5 + 2/3
0
3 the general solution to
the homogeneous
problem one particular solution
to nonhomogeneous
problem Solutions to nonhomogeneous matrix equations
Ax = b .
5
2
x2 + x3 = and x3 can be whatever.
3
3
5
2
x2 = − x3 +
3
3 • Example 3. Solve the equation 1
• so x1 − x3 =
3
1
x1 = x3 +
3 2
and
3
2
3 2/3
1
x = C −5 + 2/3
0
3 the general solution to
the homogeneous
problem one particular solution
to nonhomogeneous
problem Solutions to nonhomogeneous matrix equations
Ax = b .
5
2
x2 + x3 = and x3 can be whatever.
3
3
5
2
x2 = − x3 +
3
3 • Example 3. Solve the equation 1
• so x1 − x3 =
3
1
x1 = x3 +
3 2
and
3
2
3 2/3
1
x = C −5 + 2/3
0
3 the general solution to
the homogeneous
problem one particular solution
to nonhomogeneous
problem Solutions to nonhomogeneous matrix equations
Ax = b .
5
2
x2 + x3 = and x3 can be whatever.
3
3
5
2
x2 = − x3 +
3
3 • Example 3. Solve the equation 1
• so x1 − x3 =
3
1
x1 = x3 +
3 2
and
3
2
3 2/3
1
x = C −5 + 2/3
0
3 the general solution to
the homogeneous
problem one particular solution
to nonhomogeneous
problem Solutions to nonhomogeneous matrix equations
Ax = b .
5
2
x2 + x3 = and x3 can be whatever.
3
3
5
2
x2 = − x3 +
3
3 • Example 3. Solve the equation 1
• so x1 − x3 =
3
1
x1 = x3 +
3 2
and
3
2
3 2/3
1
x = C −5 + 2/3
0
3 the general solution to
the homogeneous
problem one particular solution
to nonhomogeneous
problem Solutions to nonhomogeneous matrix equations
Ax = b .
5
2
x2 + x3 = and x3 can be whatever.
3
3
5
2
x2 = − x3 +
3
3 • Example 3. Solve the equation 1
• so x1 − x3 =
3
1
x1 = x3 +
3 2
and
3
2
3 2/3
1
x = C −5 + 2/3
0
3 the general solution to
the homogeneous
problem one particular solution
to nonhomogeneous
problem Solutions to nonhomogeneous matrix eq...
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 Spring '13
 EricCytrynbaum
 Differential Equations, Geometry, Equations

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