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Multivariable System - Calculus - Exercise, Exercises of Calculus

National Institute of Industrial EngineeringCalculus

This file contains some problems related calculus. Some hints to the given problems are: Multivariable System, Value of the Determinant, System of Equations, Cramers Rule, Not Applicable, Gaussian Elimination, System of Equations, Answer Key

Typology: Exercises

2011/2012

Uploaded on 12/31/2012

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bg1
Multivariable Systems
Findthevalueofthedeterminant.
1)
-14-1
-42-4
34 4
A) 14 B) -94 C) -14 D) 110
2)
600
898
326
A) 420 B) 233 C) -228 D) 228
3)
123
215
123
A) 0 B) 50 C) -20 D) 1
4)
42 4
23-5
32-5
A) 10 B) -98 C) -50 D) 50
SolvethesystemofequationsusingCramerʹsRuleifitisapplicable.IfCramerʹsRuleisnotapplicable,sayso.
5)
-5x+2y-z=-
32
x-9y-4z=-
75
-2x+y+z=-
7
A) x=9
,
y=-8
,
z=-3;(9
,
-8
,
-3) B) x=9
,
y=8
,
z=3;(9
,
8
,
3)
C) x=10
,
y=6
,
z=3;(10
,
6
,
3) D) x=8
,
y=3
,
z=8;(8
,
3
,
8)
6)
4x-6y-4z=-
28
-5x+5y-6z=-
74
-9x-3y+6z=-
30
A) x=8
,
y=4
,
z=9;(8
,
4
,
9) B) x=8
,
y= -4
,
z= -9;(8
,
-4
,
-9)
C) x=4
,
y=9
,
z=4;(4
,
9
,
4) D) x=9
,
y=2
,
z=9;(9
,
2
,
9)
7)
4x+9z=48
-3x+8y+7z=75
2x-6y=-
36
A) x=4
,
y=5
,
z=4;(4
,
5
,
4) B) x=3
,
y=7
,
z=4;(3
,
7
,
4)
C) x=3
,
y=-7
,
z=-4;(3
,
-7
,
-4) D) x=7
,
y=4
,
z=7;(7
,
4
,
7)
pf3

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Multivariable Systems

Find the value of the determinant.

A) 14 B) - 94 C) - 14 D) 110

A) 420 B) 233 C) - 228 D) 228

A) 0 B) 50 C) - 20 D) 1

A) 10 B) - 98 C) - 50 D) 50

Solve the system of equations using Cramerʹs Rule if it is applicable. If Cramerʹs Rule is not applicable, say so.

  • 5x + 2y - z = - 32 x - 9y - 4z = - 75
  • 2x + y + z = - 7 A) x = 9, y = - 8, z = - 3; (9, - 8, - 3) B) x = 9, y = 8, z = 3; (9, 8, 3) C) x = 10, y = 6, z = 3; (10, 6, 3) D) x = 8, y = 3, z = 8; (8, 3, 8)

4x - 6y - 4z = - 28

  • 5x + 5y - 6z = - 74
  • 9x - 3y + 6z = - 30 A) x = 8, y = 4, z = 9; (8, 4, 9) B) x = 8, y = -4, z = -9; (8, - 4, - 9) C) x = 4, y = 9, z = 4; (4, 9, 4) D) x = 9, y = 2, z = 9; (9, 2, 9)

4x + 9z = 48

  • 3x + 8y + 7z = 75 2x - 6y = - 36 A) x = 4, y = 5, z = 4; (4, 5, 4) B) x = 3, y = 7, z = 4; (3, 7, 4) C) x = 3, y = - 7, z = - 4; (3, - 7, - 4) D) x = 7, y = 4, z = 7; (7, 4, 7)

PreCalculus

x - y + 2z = 5 2x + z = 0

  • x + y - 2z = - 25 A) x = 0, y = 0, z = - 5; (0, 0, - 5) B) x = 0, y = -5, z = 0; (0, - 5, 0) C) x = 2, y = - 5, z = 0; (2, - 5, 0) D) not applicable

Use Gaussian elimination to solve the system of equations.

  1. x + y + z = - 2 x - y + 5z = 22 5x + y + z = - 22 A) (5, - 2, - 5) B) (5, - 5, - 2) C) No solution D) (-5, - 2, 5)

  2. x - y + 5z = 6 2x + z = 1 x + 3y + z = - 2 A) (1, - 1, 0) B) (0, - 1, 1) C) No solution D) (1, 0, - 1)

  3. x - y + z = - 8 x + y + z = 0 x + y - z = 2 A) No solution B) (-1, - 3, 4) C) (-3, 4, - 1) D) (-3, - 1, 4)

  4. 2x + 2y + z = 7 4x - 4y - z = - 25 2x + y + 4z = 19 A) (5, 3, - 2) B) (-2, 5, 3) C) No solution D) (-2, 3, 5)

Calin M. Agut - 2012