The inner product of the two vectors shown is:

dot product of two vector is zero the vectors are

Let  and  be two vectors.

Let A =  a b c d , B =  e f g h ∈ M2,2(R) and define hA, Bi = ae + bf + 2cg + 2dh. (a) Show hA, Bi is an inner product of M2,2(R).

A vector 𝑥𝑥⃗ = [−1, −2𝑗𝑗, 2, 𝑗𝑗] is projected onto 𝑦𝑦⃗ = [2, 1, −𝑗𝑗, 2] to give vector 𝑧𝑧⃗.a) (2) Find the inner product < 𝑥𝑥⃗ , 𝑦𝑦⃗ >.b) (2) Find the self-inner product of 𝑦𝑦⃗.c) (2) Find the projection coefficient.d) (2) Write down the vector 𝑧𝑧⃗.

Determine which of the following vectors are equal