Applying the Alternative Form of the Gram-Schmidt Process In Exercises 49-54, apply the alternative form of the Gram-Schmidt orthonormalization process to find an orthonormal basis for the solution space of the homogeneous linear system. 2 x 1 + x 2 − 6 x 3 + 2 x 4 = 0 x 1 + 2 x 2 − 3 x 3 + 4 x 4 = 0 x 1 + x 2 − 3 x 3 + 2 x 4 = 0
Applying the Alternative Form of the Gram-Schmidt Process In Exercises 49-54, apply the alternative form of the Gram-Schmidt orthonormalization process to find an orthonormal basis for the solution space of the homogeneous linear system. 2 x 1 + x 2 − 6 x 3 + 2 x 4 = 0 x 1 + 2 x 2 − 3 x 3 + 4 x 4 = 0 x 1 + x 2 − 3 x 3 + 2 x 4 = 0
Solution Summary: The author explains the orthonormal basis for the solution space of the homogenous linear system.
Applying the Alternative Form of the Gram-Schmidt Process In Exercises 49-54, apply the alternative form of the Gram-Schmidt orthonormalization process to find an orthonormal basis for the solution space of the homogeneous linear system.
2
x
1
+
x
2
−
6
x
3
+
2
x
4
=
0
x
1
+
2
x
2
−
3
x
3
+
4
x
4
=
0
x
1
+
x
2
−
3
x
3
+
2
x
4
=
0
Find a basis for and the dimension of the solution space of the homogeneous system of linear equations
2x3
20x4
29x4
9x1
4x2
= 0
4x3
12x1 - 6x2
2x2
2x2
9x4 = 0
3x1
3X1
X3
9x4 = 0
(a) a basis for the solution space
(b) the dimension of the solution space
Apply the alternative form of the Gram-Schmidt orthonormalization process to find an orthonormal basis for the solution space of the homogeneous linear system.
X₁ + X₂
X3 - 2x4-0
2x₁ + x₂ - 2x₂ - 4x4-0
U₁
4₂
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