Consider R4 as an inner product space with the following inner product : < (a, b, c, d), (e, f, g, h) >= ae+bf+cg+dh. (a

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Consider R4 As An Inner Product Space With The Following Inner Product A B C D E F G H Ae Bf Cg Dh A 1 (24.38 KiB) Viewed 33 times

Consider R4 as an inner product space with the following inner
product : < (a, b, c, d), (e, f, g, h) >= ae + 12 bf + 13 cg
+ 14 dh. (a) Let ~v = (4,−8,−6, 4). Calculate ||~v|| in this inner
product space. (b) Determine all the vectors orthgonal to both (1,
8, 0, 8) and (1, 4,−3,−8) in this inner product space. Hint: To do
(b) take a general element from R4 and calculate its inner product
with both these vectors separately. This should result in a system
of two equations which you can then solve.
Consider R4 as an inner product space with the following inner product : < (a, b, c, d), (e, f, g, h) >= ae+bf+cg+dh. (a) Let U=(4,-8,-6,4). Calculate |||| in this inner product space. (b) Determine all the vectors orthgonal to both (1,8,0, 8) and (1,4,-3, -8) in this inner product space. Hint: To do (b) take a general element from R4 and calculate its inner product with both these vectors separately. This should result in a system of two equations which you can then solve.