Question

1-1 1 (1 2) 1.4) Find the QR decomposition of the matrix A = | 1

Answer 1

Answer:) We see that the three vectors making up A, which are

$\mathbf{a} = (1, 1, 1); \mathbf{b} = (-1,1,0); \mathbf{c} = (1,2,1)$

are linearly independent (since $\mathbf{a \cdot b \times c} \neq \mathbf{0}$ , which means they are non-coplanar, and hence independent in 3D), we can form an orthonormal basis out of them:

1. $\mathbf{\hat{e}}_1 = \dfrac{\mathbf{a}}{||\mathbf{a}||} = \dfrac{1}{\sqrt{3}}(1,1,1)$
   
2. 
   en
   
   
   
3. 
   ag-c-e1.c-ếp.c= (1,2,1)--(1,2,1)--(V3-1.2V3+2.0)= a3 аз 3' 3 аз 6v3 9
   

Now, we get that :

1/V3-1/3(V3+1) (4/3 -2/v3) 104-63 9 1/V3 -1/3 (4/3- 4/V3) 104-63 e1' e2 e3 (1-1/v3) 104-63

and also,

104 6V3 9 V3/3- 5/3 2/уз 0 ез . с (5-11/уз) 0 0 104 6y3