In order for a matrix B to be the inverse of A, both equations AB D I and BA D I must be true. b. If A and B are n n and invertible, then A 1B 1 is the inverse of AB. c. If A D a b c d and ab cd ¤ 0; then A is invertible. d. If A is an invertible n n matrix, then the equation Ax D b is consistent for each b in Rn. e. Each elementary matrix is invertible.

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What is the value of x in the figure below? if necessary, round your answer to the nearest tenth of a unit. 12 d 4 b оа. 3.1 ов. 6.9 ос. 4 od. 12

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.