What is the result of the following matrix operation? A2 = (a b; -b a) → A̅2 = (a -b; b a) → (A̅2)T = (a b; -b a) = A2. Therefore, A2 is hermitian....

What is the result of the following matrix operation? A2 = (a b; -b a) → A̅2 = (a -b; b a) → (A̅2)T = (a b; -b a) = A2. Therefore, A2 is hermitian. A3 = (a c + id i c - i 0 e + f i; -d i e - f i b) → A̅3 = (a c - id -i c + i 0 e - f i; d i e + f i b) → (A̅3)T = (a c + id i c - i 0 e + f i) = A3. Therefore, A3 is hermitian. Matrix Operations 1. Addition/Subtraction Given A and B two matrices of the same order, and α, β ∈ R scalars (real numbers), then: For A2x3 = (a b c; d e f), B2x3 = (g h i; j k m) α.A2x3 ± β.B2x3 = α.(a b c; d e f) ± β.(g h i; j k m) = (α.a ± β.g α.b ± β.h α.c ± β.i; α.d ± β.j α.e ± β.k α.f ± β.m) = C2x3 Example: Calculate 3.A - 4.B Solution: 3.A2x3 - 4.B2x3 = 3(a b c; d e f) - 4(g h i; j k m) = (3a - 4g 3b - 4h 3c - 4i; 3d - 4j 3e - 4k 3f - 4m) = C2x3 b) 7.A3x3 + 9.B3x3 - 5 Solution: 7.A3x3 + 9.B3x3 - 5 = 7.(a b c; d e f) + 9.(g h i; j k m) - 5.(1 0 0; 0 1 0; 0 0 1) = (7a + 9g - 5 7b + 9h - 5 7c + 9i - 5; 7d + 9j - 5 7e + 9k - 5 7f + 9m - 5; 7a + 9g - 5 7b + 9h - 5 7c + 9i - 5) = (2 -4 7; 3 12 -5; 8 10 0) 2. Multiplication To multiply two matrices, they must meet the following condition: Procedure: Let's try with the following matrices: A3x2 = (a b; c d; e f); B2x4 = (g h i j; k l m n) We will calculate: A3x2 . B2x4 = C3x4, if it meets the condition. = (a.g + b.k a.h + b.l a.i + b.m a.j + b.n; c.g + d.k c.h + d.l c.i + d.m c.j + d.n; e.g + f.k e.h + f.l e.i + f.m e.j + f.n; a.j + b.n c.j + d.n e.j + f.n) = (a.g + b.k a.h + b.l a.i + b.m a.j + b.n; c.g + d.k c.h + d.l c.i + d.m c.j + d.n; e.g + f.k e.h + f.l e.i + f.m e.j + f.n; a.j + b.n c.j + d.n e.j + f.n) Example: Calculate A.B Solution: A3x2 . B2x4 = (a.g + b.k a.h + b.l a.i + b.m a.j + b.n; c.g + d.k c.h + d.l c.i + d.m c.j + d.n; e.g + f.k e.h + f.l e.i + f.m e.j + f.n) = C3x4

A2 is hermitian.
A3 is hermitian.
The result of 3.A - 4.B is (3a - 4g 3b - 4h 3c - 4i; 3d - 4j 3e - 4k 3f - 4m).
The result of 7.A3x3 + 9.B3x3 - 5 is (2 -4 7; 3 12 -5; 8 10 0).
The result of A.B is C3x4.
a) All affirmations are correct.
b) Only affirmations 1, 2 and 3 are correct.
c) Only affirmations 2, 3 and 4 are correct.
d) Only affirmations 3, 4 and 5 are correct.
e) All affirmations are incorrect.