(a) compute the rank and nullity of the following matrices: 3 17 2 1) a = 0 3 -1 | 1-3 4 -2 (1 -1 b= 2 -2 4 10 0 c 3 1 1) = 6 2 2 19 3 3 ) -8 feel free to use the rank-nullity theorem. (b) determine which of the above matrices is invertible and compute their inverse clearly showing your calculations. (c) suppose that a is an m xn matrix and b is an p x m matrix satisfying rank(b) = p and null(b) = rank(a). show that null(a) = n - m + p. hint. use the rank-nullity theorem.

An apartment has a replacement cost of $950,000 and contents valued at $1,450,000. it has a classification of a and a territory rating of 3. find the annual premium a) $10,185 b) $9,230 c) $3,155 d) $13,830

Suppose you are going to graph the data in the table. minutes temperature (°c) 0 -2 1 1 2 3 3 4 4 5 5 -4 6 2 7 -3 what data should be represented on each axis, and what should the axis increments be? x-axis: minutes in increments of 1; y-axis: temperature in increments of 5 x-axis: temperature in increments of 5; y-axis: minutes in increments of 1 x-axis: minutes in increments of 1; y-axis: temperature in increments of 1 x-axis: temperature in increments of 1; y-axis: minutes in increments of 5

Mr. brettler is hanging up a 5-foot tall rectangular welcome sign in the gym. he has drawn a sketch on a coordinate grid. he has the lower vertices of the sign at (9, –3) and (–6, –3). where would the upper vertices be on the grid?