Mat 313: elements of linear algebra (page 1 of 2) (1) (20 points) let a be an nx 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 rn. (c) the null space of a is trivial, e. nul(a)-0) (d) there is only one solution to the equation ax = 0 and it is the x = 0. (e) the unique linear map ta : r" r, defined by a, is one-to-one. (f) the unique linear map ta : r"r, defined by a, is onto. (g) the rank of a is n. (h) det a 0.

[10 points, algebra 2]according to my answer key the restrictions are -1 and 4. but why not positive 1?

You have learned about the six trigonometric functions, their definitions, how to use them, and how to represent them graphically. the sine, cosine, and tangent trigonometric functions can be paired with their reciprocal functions, cosecant, secant, and cotangent, respectively. think about how each function is related to its reciprocal function.how are the graphs of the reciprocal functions related to their corresponding original functions? what happens to the graphs of the reciprocal functions as x approaches the zeros of the original functions? describe how you would teach friends with different learning styles (visual-spatial, aural-auditory, verbal-linguistic, physical-bodily-kinesthetic, logical-mathematical, social-interpersonal, and solitary-intrapersonal) how to graph the reciprocal functions

Suzanne began a trip with 18 1/2 gallons of gas in the gas tank of her car if she hughes 17 3/4 gallons on the trip how many gallons does she have left once she finish the trip