Matrices w Calculator
Solve ts matrices
(1 0 1 )
( 0 1 9)
Already in row reduced form so already solved
x= 1, y=9 or (1,9)
Given this matrix, what is the solution
(1 0 0 2 )
(0 1 0 5 )
(0 0 1 12 )
2,5,12 or x= 2, y= 5, z=12
What is A23
(2 4 7 )
( 5 2 7 )
( 1 9 3)
7
2 down 3 to the right
find the slope between
(5,0) (7,-4)
-4-0/ 7-5
-4/2
slope= -2
y= x+2
y= -x+2y
Find the point of intersection
*Find the solution
(0,2)
x+2=-x +2
2x=0
x=0
0+2=y, y=2
Solve ts Matrix
( 1 1 0 7)
(0 1 1 4)
(1 1 1 7)
(1 0 0 3)
( 0 1 0 4)
( 0 0 1 0)
Given this Marrix what is the solution
(1 -1 2 3)
(0 0 0 1)
No solution! 0x+0y+0z=1 makes no sense
What is Transpose of Matrix B
Matrix. B=
(4 )
(5 )
( 8)
(4 5 8)
row 1 becomes column 1
Write this in slope-intercept form
2= 2y+x
2=2y+x
2-x=2y
y= -x/2 +1
Find the solution/ point of intersection
y= 3x -20
y= 6x-2
x= -6 , y =-38
(-6,-38)
Solve ts Matrix
(2 1 3)
(4 0 6)
(1 0 1.5)
( 0 1 0)
Solve and write down the solution
(1 2 4)
(2 4 8)
(1 2 4)
(0 0 0)
(4-2t,t)
or
(t,2-.5t)
(2 3) - 2 * (-5 7)
(7 8) (4 -6)
(12 -11)
(-1 20 )
remember distributive property
2 methods
Don't distribute minus
(2 3) - (-10 14)
(7 8). (8 -12)
or
Distribute minus
(2 3) + (10 -14 )
(7 8) ( -8 12)
Write an equation with a slope of 2 that goes through the point (10, 25)
2 *10 =20
y=20+5
y=2x+5
2y+3x= 3
x=1, y=0
(1,0)
Solve ts Matrix
(1 1 1 2)
(2 2 2 5)
(1 1 1 2)
(0 0 0 1)
no solution because 0x+0y+0z cannot =1
Solve ts and write the solution down
(1 2 3)
(2 4 6)
(1 2 3)
(0 0 0)
solution is
(3-t,t)
or
(t, 1.5-0.5t)
A transpose + B
A =
(9 5)
(6 9)
B=
(4 2 )
(8 1)
(9 6). + (4 2). = (13 8 )
(5 9). ( 8 1). (13 10)
remember to transpose
The cost of making a Dr. Pepper bottle is 50 cents. Dr. Pepper sells its bottles for 2 dollars. Dr. Pepper has to pay 6000 dollars a month for their factory rent. Find the cost, revenue equation, profit equation, and the break-even point.
Cost= .5x+ 8000
Revenue= 2x
Profit=1.5x -6000
break-even point x= 4000
x+y=5
2x-y=1
x=2, y=3
(2,3)
Solve ts matrices
(6 7 6 7)
(7 6 7 6)
(6 7 6 7)
1 0 1 0
0 1 0 1
0 0 0 0
extra 100 points for writing the solution
t,1,s
What is the solution
(1 2 0 1 3)
(0 0 1 -1 2)
(0 0 0 0 0)
(0 0 0 0 0)
w,x,y,z
(3-t-2s, s, 2+t, t)
(3u 2z ) + ( 2 5 ) (8 7 )
(2 4 ). ( 3x 4y). (14 16)
u= 2
x= 4
y= 3
z= 1
3u+2= 8
2z+5= 7
2+3x= 14
4+4y= 16
Mrs. K buys a Cybertruck for 46 bands (46,000). The scrap value at 10 years is 1,000 dollars.
What is the equation for this depreciation, and what is the value at 2 years
-4500x+46000
at 2 years 37000
x+y=z=6
2x-y+z= 3
x+2y-z= 2
x=1, y=2,z=3
(1,2,3)