Question

The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W. Assume the vectors are in the order bold x1 and bold x2
1 7
-4 -7
0 -6
1 1
The orthogonal basis produced using the Gram-Schmidt process for W is:__________. (Use a comma to separate vectors as needed.)

Answer 1

Answer:

$y_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right]$  ,  $y_2 = \left[\begin{array}{ccc}5\\1\\-6\\-1\end{array}\right]$

Step-by-step explanation:

$x_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right]$    and $x_2 = \left[\begin{array}{ccc}7\\-7\\-6\\1\end{array}\right]$

Using Gram-Schmidt process to produce an orthogonal basis for W

$y_1 = x_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right]$

Now we know X₁ , X₂ and Y₁

Lets solve for Y₂

$y_2 = x_2- \frac{x_2*y_1}{y_1*y_1}y_1$

see attached for the solution of Y₂