18. Suppose R^2 has weighted inner product given as <u, v> =(3u base 1 v base 1 + 2u base 2 V base 2 for u = (u base 1, u base 2), v = (V base 1, v base 2). Let u = (1, 2), v = ( 2, - 1) and K = 3. Then the valued of <u, kv> is.....
(i) 4
(ii) 6
(iii) 18
(iv) None
19. Suppose that u, v V are such that ||u|| = 2, ||u +v|| = 3 and ||u - v|| = 4. Then ||v|| is?
(i) 17/2
(ii) √17
(iii) Does not exist
(iv) None
20. For a given matrix A=, the matrix P that is orthogonally diagonalizes A is of the following matrices are diagonalisable
(i)P=
(ii)P=
(iii)P=
18.
Answer: (ii) 6
19.
then:
Answer: (iii) Does not exist
20.
first eigenvector:
second eigenvector:
Answer:
(i)P=
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