Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Mat 117 Problem set 6 (System of Equations) Write your name and date 1. Solve the following systems of equations: a) 3x y 8 15 x 2 y 26 a) solution x , y Write your answer here: b) Many solutions {( x, y) | x , y any real number} c) No solution b) 3x y 8 15 x 5 y 13 a) solution x , y Write your answer here: b) Many solutions {( x, y) | x , y any real number} c) No solution c) 5x y 8 15 x 3 y 24 a) solution x , y Write your answer here: b) Many solutions {( x, y) | x , y any real number} c) No solution 2. Use matrix method (Augmented form) and solve the following systems: a) x 3 y 4 z 21 2x y z 7 2 x 3 y 3z 19 a) solution x , y , z Write your answer here: b) Many solutions {( x, y, z ) | x , y,z any real numbers} c) No solution b) x 2 y 6 4z x 13z 6 y 2 x 4 y 8 z 12 Write your answer here: a) solution x , y , z b) Many solutions {( x, y, z ) | x , y= , z is any real number} c) No solution 3. Identify if the order triple (1, 2,3) is a solution of the given system of equations. 3x 5 y z 16 7 x y 3z 4 x 5 y 7 z 10 4. Identify if the system of equations given below has unique solution, infinitely many solutions, or no solution. 2 x 5 y 16 3x 7.5 y 24 5. Given is the augmented matrix of a system of equations: 1 5 6 2 7 1 3 5 1 5 7 13 Write the new form of the augmented matrix after the following row operations. R1 r1 r3 , R2 r2 7r3 6. Four times the number of white marbles exceeded 9 times the number of red marbles by 10. The ratio of blue marbles to red marbles was 3 to 1. There is a total of 65 marbles of all 3 colors. Form a system of equations with variables red marble: r, white marble: w, and blue marble: b. Use inverse matrix method to solve the system and determine how many are white, haw many are red and how many are blue marbles.