Part A. Each system of equations in this section consists of a system of 3 lines
ID: 2960846 • Letter: P
Question
Part A. Each system of equations in this section consists of a system of 3 lines in R2.
-x+4y=8
y=2
A2. 2x+3y=6
-x+4y=8
y=-2
A3. -x+4y=8
x-4y=8
-3x+12y=24
A4. -x+4y=8
x-4y=-8
-2x+12y=12
Part B. Each system of equations in this section consists of 2 equations of planes in R3.
B1: 2x+3y+4z=6
-x+4y+6z=8
B2: -x+4y+6z=8
x-4y+6z=9
B3: -x+4y+6z = 8
x-4y-6z=-8
For each question without using liner algabra just calcules:
(a) State whether there are no solutions, infinitely many solutions or just one solution.
(b) Draw a graph that illustrates the lines or planes and their solution set. (For planes you can approximate.)
(c) Show a calculation that finds the unique solution, describes the infinitely many solutions or explains why there are no solutions.
(d) If the system has infinitely many solutions, symbolically describe the solution set using both a traditional line/plane equation and a vector equation for a line/plane.
Each system of equations in this section consists of a system of 3 lines in R2. 2x+3y=6 -x+4y=8 y=2 2x+3y=6 -x+4y=8 y=-2 -x+4y=8 x-4y=8 -3x+12y=24 -x+4y=8 x-4y=-8 -2x+12y=12 Each system of equations in this section consists of 2 equations of planes in R3. 2x+3y+4z=6 -x+4y+6z=8 -x+4y+6z=8 x-4y+6z=9 -x+4y+6z = 8 x-4y-6z=-8 For each question without using liner algabra just calcules: State whether there are no solutions, infinitely many solutions or just one solution. Draw a graph that illustrates the lines or planes and their solution set. (For planes you can approximate.) Show a calculation that finds the unique solution, describes the infinitely many solutions or explains why there are no solutions. If the system has infinitely many solutions, symbolically describe the solution set using both a traditional line/plane equation and a vector equation for a line/plane.Explanation / Answer
A1 unique solution as number of variable = number of nonzero row.
A2 no solution as both side corresponds different value
A3 infinite solution as number of variable is more that non zero row.
A4 no solution