Questions on Algebra: Linear Algebra (NOT Linear Equations) answered by real tutors!

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Question 1122624: Let u and v be non-zero vectors in R^3 in standard position. Prove that if u and v are of length rcm each, where r is an element of R and r is greater than 0, then their tips lie on the surface of a sphere of radius rcm.
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Question 1122633:
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Question 1122638: The slope of the tangent line to the graph of a cubic polynomial is -24 at two different points: (-2,79) and (1,-20). Determine the equation of the cubic polynomial.
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Question 1122649: Write the system of linear equations in the form Ax = b and solve this matrix equation for x.
2x1 − x2 + x4 = 9
3x2 − x3 − x4 = −9
x1 + x3 − 3x4 = −2
x1 + x2 + 2x3 = 0

Click here to see answer by ikleyn(52775)

Question 1122637: Determine the solution set for the following system. If infinitely many solutions, express answer in terms of t and s.
2x1-3x2+x3-7x4=23 (These are sub numbers)
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Question 1122648: Write the system of linear equations in the form Ax = b and solve this matrix equation for x.
x1 − 5x2 + 2x3 = −11
−3x1 + x2 − x3 = 10
−2x2 + 5x3 = 1

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Question 1122472: Consider the following points.
(−2, 48), (−1, 0), (0, −16), (1, −18), (2, 0)
(a) Determine the polynomial function of least degree whose graph passes through the given points.
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Question 1123288: -4|2x+1|-3=-15
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Question 1123319: What is f(g(x)) and g(f(x)). f(x)= 2x^2+1, g(x)= 2x-1
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Question 1123317: What is f(g(x)) and g(f(x)). f(x)=2x-2, g(x)= 3x^2+1
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Question 1123361: f(x)=2x-1,g(x)=x^2+2. What is f(g(-1))?

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Question 1123361: f(x)=2x-1,g(x)=x^2+2. What is f(g(-1))?

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Question 1123480: 3x+7=5z,
3x+5y=3,
3z-3y=2.
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Question 1123488: 3x+7=5z,
3x+5y+3,
3z-3y+2.

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Question 1123009:
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Question 1123817: -8x+5y=0
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Question 1123823: The length of a rectangle field is 42 meters more than the width. Its perimeter is 600 meters. Find the dimensions.
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Question 1123975: For the function f(x) = −5x^3 + 3x^5 , find all critical values and determine whether each represents a local maximum, local minimum or neither. Then find the absolute extrema on the interval [−2, 2].
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Question 1124145: Previous question was not written correctly. Correct question should read Suppose that the cost function for the production of a particular item is given by the function C(x)=2x second power -320x + 12,020, where x represents the number of items. How items should be produced to minimize the cost? Explain your answer.
Click here to see answer by MathLover1(20849)

Question 1124399: Write the equation in slope-intercept form of the line parallel to
7x − 5y =− 20 going through the point (5, 2) .

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Question 1124806: n=3
3 and 4i are zeros
f(1) = 68
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Question 1124833: which quadrants does the inequality have solutions y>3|x|+1
A 1,2,3,4
B 1,2
C 1,3,4
D 1
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Question 1124833: which quadrants does the inequality have solutions y>3|x|+1
A 1,2,3,4
B 1,2
C 1,3,4
D 1
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Question 1124947: Eight prizes are to be given to eight different people in a group of fourteen. In how many ways can a first prize, a second prize, a third prize and five fourth prizes be given?

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Question 1125200:
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Question 1125816: Plan A $39.99 for 200 min and $1.25 for each min after how can i slove the problem
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Question 1126299: Rapid Rental car company charges a $55 dollar rental fee and $0.25 per mile driven. For the same car, Capital Cars charges $45 for a rental fee and $0.35 per mile. write an equation and find the number of miles for which the companies will be charged the same
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Question 1126445: i need help with vectorial spaces. how do you check if a generated subspace is a base
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Question 1127206: system of equations:
Alysha is two years younger than Bryce. The sum of their ages is 28. How old is Alysha?
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Question 1127206: system of equations:
Alysha is two years younger than Bryce. The sum of their ages is 28. How old is Alysha?
Click here to see answer by Alan3354(69443)

Question 1127158: Solve for x, y and z using cramer's rule
3x + 4y -z =7 , 7x +2y -8z = -83 , x-8y + 9z =49
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Question 1127223: g(x)is a horizontal compression of f(x) by a factor of 1/7
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Question 1127337: If a^2-1/a=1 find the value of a^6-1/a
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Question 1127616: If we put a cool object into a preheated oven, Newton's law of heating tells us that the difference between the temperature of the oven and the temperature of the object decreases exponentially with time. The percentage rate of decrease depends on the material that is being heated. Suppose a potato initially has a temperature of 75 degrees and the oven is preheated to 375 degrees. Use the formula
D = 300 � 0.98t,
where D is the temperature difference between the oven and the potato, t is the time in minutes the potato has been in the oven, and all temperatures are measured in degrees Fahrenheit.
What is the temperature of the potato after 20 minutes? (Round your answer to the nearest degree.)
- I'm slightly confused by this problem because when I put D=300 times 0.98^20 it gives me 200 and it says this answer is wrong. What am I doing wrong is 20 not what i plug in for t?
Click here to see answer by josmiceli(19441)

Question 1127709: While I can solve for y, I believe I'm missing something with the absolute value sign. There are pipes on the left side of the equation around the whole fraction. I think it changes the whole solution. Can someone elaborate please?
| | = 2
Click here to see answer by MathLover1(20849)

Question 1127708: Okay I have no idea where to post this but, I also have no idea whats going on here.
'Resolve the following equation for B2.' [Note: the numbers are subscript]
A1/B1 = A2/B2
What in the world is this supposed to be? I feel like it's really simple but I'm just missing it. All the numbers are subscript.
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Question 1127871: If i'm getting this right, there is no solution except (- infinity, infinity) ?
The J has a SUBscript 0 next to it. 'Solve the following equation for b.'

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Question 1127884: Clarifying - Looking to solve b here, the 0 after J is subscript:

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Question 1128465: Exploit the following pair of functions h and k to find (h/k) (x) if it exists.
,
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Question 1128603: You want to get rid of the y by elimination in the system below: x-6y=35;
10x-2y=35. If you multiply the top equation by 4, by which number will you multiply the bottom equation?

Click here to see answer by Alan3354(69443)

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