(3 points) (Orthonormal Bases/Gram-Schmidt) Consider the matrix A=[ a
.1
​
​
a
33
​
​
a
.1
​
​
]= ⎣
⎡
​
1
0
0
​
2
0
3
​
4
5
6
​
⎦
⎤
​
. (a) Find an orthonormal basis { q
​
1
​
, q
​
2
​
, q
​
3
​
} for the columns of the matrix A. (b) Find the matrix R for which A=QR, i.e., the matrix which expresses the vectors a
1
​
, a
2
​
and a
3
​
as linear combinations of the orthonormal basis vectors. (Hint: what is the inverse of Q, as discussed in class?). (c) From the result above, find the constants c 11
​
,c 12
​
and c 13
​
for which a
1
​
=c 11
​
q
​
1
​
+c 12
​
q
​
2
​
+c 13
​
q
​
3
​
.