(1) (20 points) let a be an n x n matrix. determine which (if any) of the statements are equivalent to the statement the matriz a is invertible. (a) the columns of a are linearly independent. (b) the columns of a span r". (c) the null space ofa is trivial, ie. nul(). (d) there is only one solution to the equation ax = 0 and it is the x = 0. (e) the unique linear map ta : rn ? rn, defined by a, is one-to-one. ) the unique linear map ta : rn ? rn, defined by a, is onto. (g) the rank of a is n. j (h) det a0.

the figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing im pretty sure that is the right answer

step-by-step explanation:

answer: -1

step-by-step explanation:

i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

hope i could ! : )