Elementary Rows Rank and number of solution.1)1-22 3-1[A|b] =-3-11-72 -45 8-4Number of unknown variables n =Rank of A =Rank of [A|b] =Number of solution set2)-83-244 -17-5-122 -12[A|b] =4-1-3-27-2-121-3-2 0 0 11-4Number of unknown variables n =Rank of A =Rank of [A|b] =Number of solution set3)1324 -1[A|b] =0 -3324 -12 -2Number of unknown variables n =Rank of A =Rank of [A|b]Number of solution set2.

Answered: 1) 1 -2 2 3 -1 [A]b] = -3 -1 1 -7 -4 5…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 21RE

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U.S. Energy Consumption Energy consumptionin the United States in quadrillion BTUs can bemodeled by C(x) = -0.013x2 + 1.281x + 67.147,where x is the number of years after 1970.a. One solution to the equation 87.567 = -0.013x2 +1.281x + 67.147 is x = 20. What does thismean?b. Graphically verify that x = 20 is a solution to87.567 = -0.013x2 + 1.281x + 67.147.c. To find when after 2020 U.S. energy consumptionwill be 87.567 quadrillion BTUs according to themodel, do we need to find the second solution tothis equation? Why or why not?
1. -7 x -6 + (-4)2 /(-22) 2. (-6)2 /9-(5-8) x 4 3. (-2a)3x(3a/5b)2 /(-4a2b) 4. 1-2a/2 + 6a-1/6 5. 7x+3/4 - 3x-1/2 6. x-(2x+1/3)=5 solve for x 7. x+2y=10, (x/3)-(y/2)=1 solve for x and y 8, x:y=1/3:1/4, -12x+7y=-6 9. 3/x - 4/y = -1/6, 6/x + 2/y = 11/12
Let (c1, c2) be a solution of the 2 × 2 system a11x1 + a12x2 = 0 a21x1 + a22x2 = 0 Show that for any real number α the ordered pair (αc1, αc2) is also a solution.
x1+3x3+4x5=4 x2-x3+4x5=7 x4+2x5=5 Find the solution, if possible. (If there are infinitely many solutions, express x1, x2, x3, x4, and x5 in terms of the parameters s and t. If there is no solution, enter NO SOLUTION.
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Illustrate Theorems 9.2 and 9.4 on the system Theorem 9.2 A system of linear inequalities and equations is unsolvable if and only if it is inconsistent. Theorem 9.4 Every unsolvable system of linear inequalities in n variables contains an unsolvable subsystem of at most n + 1 inequalities.
Determine whether the statement below is true or false. Justify the answer. The homogenous equation Ax=0 has the trivial solution if and only if the equation has at least one free variable.
If a, b, c are real numbers and b different from 0, find the relationships between a, b, c and the numbers q, r and s for which the linear systemAX+BY=CQR+RY=S(a) has no solutions.(b) has infinitely many solutions.(c) has exactly one solution.
Numerous engineering and scientific applications require finding solutions to a set of equations. Ex: 8x + 7y = 38 and 3x - 5y = -1 have a solution x = 3, y = 2. Given integer coefficients of two linear equations with variables x and y, use brute force to find an integer solution for x and y in the range -10 to 10. Ex: If the input is: 8 7 38 3 -5 -1 Then the output is: 3 2 Use this brute force approach: For every value of x from -10 to 10 For every value of y from -10 to 10 Check if the current x and y satisfy both equations. If so, output the solution, and finish. Ex: If no solution is found, output: No solution You can assume the two equations have no more than one solution. Note: Elegant mathematical techniques exist to solve such linear equations. However, for other kinds of equations or situations, brute force can be handy.
1 0 5 -2 0 1 4 1 0 0 0 0 Row 1 - x1 + 0x2 + 5x3 = -2 Row 2 - 0x1 + x2 + 4x3 = 1 Row 3 - 0 = 0 Find the solution, if possible (if there are infinitely many solutions, express x1, x2, and x3 in terms of the parameter t. If there is no solution, enter NO SOLUTION) (x1, x2, x3) =
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1) 1 -2 2 3 -1 [A]b] = -3 -1 1 -7 -4 5 8 -4 Number of unknown variables n = Rank of A = Rank of [A|b] = Number of solution set 2) -8 3 -2 4 4 -17 -5 -1 2 2 -12 [A|b] = 4 -1 -3 -2 7 -2 -1 1 -3 -2 0 0 1 1 -4 Number of unknown variables n = Rank of A = Rank of [A|b] = Number of solution set