Write in the correct letter(s) for the possible answers given below. DEFINITION.

Question

Write in the correct letter(s) for the possible answers given below. DEFINITION. An operator T:V rightarrow W where V and W are vector spaces over the same field K is linear if for ail alpha, beta K and we have 57. THEOREM The operator L: (R,R) (R,R) defined by L[y] = yn + 2y' + 6y.is a linear operator. Proof. By the above definition, to show that the operator L is a linear operator, we must show that if c, and c2 are constants in R and (x) and (x) are functions in (R,R), then 58. Since this is an identity, we can use the standard format for proving identities.

Explanation / Answer

57 - (A) & (B) [Note: (E) can also be the answer as it can be derived from (A) & (B).]

58 - (BD)

59 - L[c11(x)+c22(x)]

[NOTE: Possible answers (DE) & (ABC) are same. It is a typo. In one of these options, 'L[c11(x)+c22(x)]' should be there.]

60 - ADE (Defnition of L)

61 - ABE

62 - ABC or DE (both are same as explained in the Note)

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