Question 908650: Create coefficient matrix and augmented matrix for the following:
Given the formula y= a(t^2) + bt + c, we can find the height, y, of an item thrown into the air. If an item is thrown and is at height, y= 23/4 at time, t= 1/2 and is at y= 7 at t= 1, and is at y= 2 at t= 2, solve for the coefficients a, b and c.
Found 2 solutions by ewatrrr, richwmiller:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website! 1/4a + b/2 + c = 23/4
.....
4a + 2b + c = 2
a + b + c = 7 Subtract 2nd from 1st EQ
3a + b = -5
..........
a + b + c = 7
1/4a + b/2 + c = 23/4 Subtract 2nd from 1st EQ
3/4a= -5/4
..............
3a + b = -5
3/4a + 1/2b = -5/4|multiplying thru by -2 to eliminate the b variable by adding the Eqs
3/2a = = -15/2
a = -5, b = 10  and c = 2 
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! coefficient matrix
.25,.5,1
4,2,1
1,1,1
coefficient matrix
augmented decimals
.25,.5,1|5.75
4,2,1|2
1,1,1|7
augmented fractions
.25,.5,1,5.75
4,2,1,2
1,1,1,7
divide row 1 by 0.25
1,2,4,23
4,2,1,2
1,1,1,7
add down (-4) *row 1 to row 2
1,2,4,23
0,-6,-15,-90
1,1,1,7
add down (-1) *row 1 to row 3
1,2,4,23
0,-6,-15,-90
0,-1,-3,-16
divide row 2 by -6
1,2,4,23
0,1,-15/-6,15
0,-1,-3,-16
add down (1) *row 2 to row 3
1,2,4,23
0,1,5/2,15
0,0,-1/2,-1
divide row 3 by -1/2
1,2,4,23
0,1,5/2,15
0,0,1,2
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (-5/2) *row 3 to row 2
1,2,4,23
0,1,0,10
0,0,1,2
add up (-4) *row 3 to row 1
1,2,0,15
0,1,0,10
0,0,1,2
add up (-2) *row 2 to row 1
1,0,0,-5
0,1,0,10
0,0,1,2
final
1,0,0,-5
0,1,0,10
0,0,1,2
"-5","10","2"
(-5,10,2)
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