Create a random matrix M and compute d1 = I + M and d2 = I - M, where I is the identity matrix. Matrices d1 and d2:

a.Their sum is zero.

b.are equal

c.Commute (two matrices A and B commute if AB is equal to BA)

d.the one is the transpose of the other

e.the one is the inverse of the other (their product is the identity matrix)

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Define a large vector (100,000 or more) such that Each element is the sum of two random numbers generated by rand. To create such a vector add two vectors that were created by two calls to rand. What is the standard deviation of such a vector.

a.Very close to the inverse square root of 12

b.Very close to the inverse square root of 6

c.Very close to 1/3

d.Very close to 1/

e.Anywhere between 0 and 1

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Compute the standard deviation of a large vector (100,000 or more) created by randn. What is this standard deviation.

a.Very close to the inverse square root of 12

b.Very close to 1

c.Anything between -1 and 1

d.Anything between 0 and 1

e.Very close to zero