Are the following statements true or false?
1. finding an eigenvector of a might be difficult, but checking whether a given vector is in fact an eigenvector is easy.
2. if ax=λx for some vector x, then λ is an eigenvalue of a.
3. a number c is an eigenvalue of a if and only if the equation (a−ci)x=0 has

Adriana sold 50 shares of a company’s stock through a broker. the price per share on that day was $22.98. the broker charged her a 0.75% commission. what was adriana’s real return after deducting the broker’s commission? a. $8.62 b. $229.80 c. $1,140.38 d. $1,149.00

Simplify 15(x - 4)(x -1)-3(x + 4)(x - 1) with steps

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.