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1. find the inverse of the following matrix A, if possible, check that A times A^-1=| and A^-1
times A=|
A= [4, 3]
[4, 4]
Answer:
2. find the inverse of the following matrix A, if possible, check that A times A^-1=| and A^-1 times A=|
A= [6, 4]
[2, 7]
Answer:
𝟕
𝟐
−
𝟏𝟕 )
( 𝟑𝟒
𝟏
𝟑
−
𝟏𝟕 𝟏𝟕
3. A system of equations is given, together with the inverse of the coefficient matrix, use the inverse of
the coefficient to solve the system of equations.
2x+7y=4
A^-1= [11, -7]
3x+11y=2
[-3, 2]
Answer:
X = 30 , y = -8
4. solve the following system of equations by using the inverse of the coefficient Matrix A
(AX=B) x+7y= -23
-3x+3y=-27
The inverse of Matrix a, a^-1 is ?
Answer:
𝟏
𝟕
−
𝟐𝟒)
(𝟖
𝟏
𝟏
𝟖 𝟐𝟒
The solution of the system is ?
Answer: (5,-4)
5. Evergreen landscaping bought 8 tons of topsoil, 5 tons of mulch, and 2 tons of pea gravel for $3381.
The next week the firm bought 5 tons of top soil, 4 tons of mulch, and 5 tons of pea gravel for $3118.
Pea gravel costs $22 less per ton than topsoil. Find the cost for each item.
Answer:
Topsoil = $244
Mulch = $197
Pea Gravel = $222
6. Evaluate the determinant
|x^4, 6|
|x^5, x^6|
Answer: x10-6x5
7. find M(12) or Mv12
A=[10, 6, 2]
[3, 3, -2]
[0, 1, 5]
Sorry, I do not understand the meaning of M
8. find the determinant of this 3x3 matrix using expansion by minors about the first column
A= [4, 6, -3]
[7, 0, 1]
[8, 5, -2]
Answer: 7
9. solve using cramer's rule
4x+8y=-3
2x+2y=-4
Answer:
x = -13/4 and y = 5/4
10. solve using cramer's rule
6x+6y=13
7x+2y=5
Answer:
X = 2/15 and y = 61/30
11. solve using cramer's rule, type as ordered triple
6x+4y+5z=-2
-7x+6y+5z=3
-4x+6y+4z=-4
Answer:
x = -1 , y= -4 , z=4
14. graph the inequality on a plane
y > x-3
Answer:
15. graph the inequality on a plane
5x+6y < 30
Answer:
19. grpah the system of inequalities
x+y < 4
x-y < 6
Answer:
20. find the max and min values of the objective function P, subject to the conditions below.
P=13x-3y+14
8x+4y < 32
0<y<5
0<x<3
Answer: min is -1 and max is 53
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