(1 point) suppose that aa is an n×mn×m matrix of rank 4,4, the nullity of aa is 2,2, and the column space of aa is a subspace of r8r8. Find the dimensions of aa.

Program using c++ only on visual studio pig is a simple two player dice game, played with one die. the first player to reach or surpass 50 is the winner. each player takes a turn rolling the dice. they add to the pot with each roll, having to decide to roll again and increase the pot, or cash out. the risk being they could lose the amount they’ve accumulated into the pot. the rules for each player’s die roll. 1. roll the dice. a. if user rolled a 1, i. the pot gets set to zero ii. the other player goes to step 1. b. a roll of 2-6 is added to the pot. 2. user can choose to hold or roll again. a. choice roll. return to step 1. b. choice hold. i. increment player score by the pot amount. ii. pot gets set to 0. iii. second player gets to roll and goes to step 1. program requirements: ● before each opponent begins ○ output the score for the person and the computer. ○ output the opponents whose turn is beginning and ask the user to hit enter to continue. ● with each dice roll. ○ output the die value, and amount of the round pot. ○ if it’s the users roll ask if they want to roll again ( r ) or hold ( h ). your program should allow r, r, h or h as valid input. if input is anything else, ask the user again until valid input is obtained. ○ the ai will continue playing until the round pot is 20 or more. ● once a player’s score is greater or equal to 50 then they have won, it will no longer ask if they want to keep rolling the die or not. ● once there is a winner ○ score totals are output along with who the winner was. user or computer ○ player is asked if they want to play again y or n. valid input should be y, y, or n, n. ● when a new game starts the starting roll goes to the player that did not roll last. if the user rolled last in the previous game, then the computer rolls first and vice versa. when the program first begins, the player will make the first roll of the first game. development notes : ● you will need a way to roll dice in your program. the rand() function works well, but returns an integer. if we want numbers 0 – 9 we can get the value modulus 10. ● call srand() with a value to seed it. it’s common to seed it with the current computer clock, include ctime, and then call srand(time(

This graph compares the cost of room and board at educational institutions in texas.

How would you categorize the software that runs on mobile devices? break down these apps into at least three basic categories and give an example of each.