a) Matrix A has elements a11 = 1+1, a12 = 1-i, azı = 1-1, a22 = 1+i Show that if Matrix A is divided by 2 then it will become Unitary Matrix.

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Q: can you show part b) closed under scalar multiplication with matrices?

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Q: snip

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Q: D If A is a square matrix and B= A". (A - A"). A show that matrix B is an inverse symmetric matrix.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: Number 6 (b and d only!)

A: We have to find the invertible matrix Q

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Q: Use the Gaussian algorithm to determine the inverse matrix A^-1.   A = 1  2  1 0  1   3 2  4   1

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Q: S)Give an example of a matrix A such that A2 = I but A#I or A± -I.

A: There are so many examples.

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A: Given  A=2-2222  and  B=222-22. We have to show that  AB=BA.

Q: Use 8 ;] 0 y = -x, ON 9 -2 -5 -2 -5 2 -8 9-1 OB) 8-9 2 09112 -2 s -9 5 OD) -5 0¹/2²/ -25 12 DO 2 to…

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Q: Calculate matrix representation based on standard bases

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Q: 2rị + 13 T: R' → R?, T 21, 22, 13, L4 ER -12 - 3r4

A: Given  and the standard bases are given by

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Q: Define Antisymmetric matrix.

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Q: Define invertible matrix.

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Q: 0 -1 and whose nullspace Construct a matrix whose column space contains 2 and 522 2 ] contains

A: Explanation is given below:Explanation:

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