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Apply the alternative form of the Gram-Schmidt orthonormalization process to find an orthonormal basis for the solution space of the homogeneous linear system. $x_1 + 4x_2 - 2x_3 - 3x_4 = 0$ $2x_1 + x_2 - 4x_3 - 6x_4 = 0$ $u_1 = $ $u_2 = $

          Apply the alternative form of the Gram-Schmidt orthonormalization process to find an orthonormal basis for the solution space of the homogeneous linear system.
$x_1 + 4x_2 - 2x_3 - 3x_4 = 0$
$2x_1 + x_2 - 4x_3 - 6x_4 = 0$
$u_1 = 
$
$u_2 = $
        
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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 + 4x2 - 2x3 - 3x4 = 0
2x1 + x2 - 4x3 - 6x4 = 0
u1 =
u2 =

Added by Anthony C.

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Elementary and Intermediate Algebra
Elementary and Intermediate Algebra
Alan S. Tussy, R. David Gustafson 5th Edition
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Apply the augmented form of the Gram-Schmidt orthonormalization process to find an orthonormal basis for the solution space of the homogeneous linear system. x + x - 2x^3 - 3x^4 = 0, Zx + x - 4x = 6x = 0.
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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 - 2x3 - 4x4 = 0

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Transcript

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00:01 In the given question, we have to find the ortho -normal basis where we have the given linear system is x1 plus x2 minus x3 minus 2 times x4 is equal to 0.
00:28 We will take it as equation number 1.
00:31 Then 2 times x1 plus x2 minus 2 times x 3 minus 4 times x 4 is equal to 0.
00:40 As equation number 2.
00:41 Now we will multiply the equation 1 by 2 and subtract the equation 1 minus equation second.
01:00 Therefore we have 2 times x1 plus 2 times x2 minus 2 times x3 minus 4 times x4 is equals to 0 minus 2 times x1 minus 2 times x2 plus 2 times x3 plus 4 times x4 is equal to 0.
01:25 Simplifying this operation we get the value of x2 is equal to 0.
01:32 Therefore the equation 1 will give us the value of x1 is equal to x3 plus 2 times x3 now let we will substitute x3 is equal to s and x4 is equal to t.
01:49 Therefore we get the value of x1 is equal to s plus 2 times t and we have the value of x2 is equal to 0...
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