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Tutors Answer Your Questions about Matrices-and-determiminant (FREE)
Question 1189235: DENTAL FILLINGS Dentists use various amalgams for silver fillings. The matrix shows the percent's (expressed as decimals) of powdered alloys used in preparing three different amalgams. Suppose a dentist has 5483 grams of silver, 2009 grams of tin, and 129 grams of copper. How much of each amalgam can be made?
PERCENT ALLOY BY WEIGHT
Amalgam
A
B
Silver
Tin
0.70
| 0.26
0.04
matrix 2&0.73\\ 5&0.27\\ 3&0.00 matrix ]
Copper
Click here to see answer by josgarithmetic(39614)  |
Question 1182632: Given the representation matrix of a linear transformation over the basis B, how to find a basis for a different representation matrix for the same linear transformation in which a certain condition is required?
For example:
V = R2[x] (all the polynomials of power 2 or less over Real numbers)
Given the following basis:
B= {1, 1+x, x^2 -1}
Defining T: V -> V a linear transformation as following:
T(1) = 4 - 3x^2
T(1+x) = 4 + 4x + 3x^2
T(x^2 -1) = x^2 - 4
The representative matrix of T is:
1 3 -3
0 4 0 = [T]B
-3 3 1
If given that T is diagonalizable, and the eigenvalues of it are { 4, 4, -2}
Find a basis of V for which the representation matrix is a diagonal matrix.
Click here to see answer by CPhill(1959)  |
Question 1181409: Given the following matrices over Z5:
b1 b4 b7
b2 b5 b8 = B
b3 b6 b9
r(B)= 3
For easier understanding letβs say that bi is the column i in matrix B.
A is a matrix of dimensions 3x3 in which the following exists:
K = { (b1+b3) , (2b2-b3) } is a basis for the equation: Ax=0.
r(A)=1
Also:
1 2 4
3 1 2 =A*B
1 2 4
r(AB)=2.
1) find a vector basis for the vector space that is Aβs columns.
2) given the following:
K = { (1,2,0) , (0,1,1) }
Find a reduced echelon form (C) for A.
Click here to see answer by CPhill(1959) |
Question 1181408: Given the following matrices:
b1 b4 b7
b2 b5 b8 = B
b3 b6 b9
r(B)= 3
For easier understanding letβs say that bi is the column i in matrix B.
A is a matrix of dimensions 3x3 in which the following exists:
K = { (b1+b3) , (2b2-b3) } is a basis for the equation: Ax=0.
r(A)=1
Also:
1 2 4
3 1 2 =A*B
1 2 4
r(AB)=2.
1) find a vector basis for the vector space that is Aβs columns.
2) given the following:
K = { (1,2,0) , (0,1,1) }
Find a reduced echelon form (C) for A.
Click here to see answer by CPhill(1959) |
Question 1178478: This question requires a confusion matrix. I am unsure how to calculate the accuracy given the percentages. How do I go about this? Thanks. :)
Both model A and model B achieves 80% accuracy on the balanced population, but changes to 64% and 96% accuracy respectively on the true unbalanced population. If the population is more skewed with 5% positive and 95% negative, what are the accuracies for each model?(The training population is 1,000 and the confusion matrix for model A is [500 200]
[0 300]
The confusion matrix for model B is [300 0]
[200 500]).
Click here to see answer by CPhill(1959) |
Question 1177662: The verbiage in this question is confusing me so much that I don't even know where to start. Any help in explaining and solving would be greatly appreciated.
The following table shows the amount spent by four U.S. airlines to fly one available seat 1 mile in the second quarter of 2014. Set up a system and then solve using technology.
// The table shows:
Airline ==> United Continental - American - Jet Blue - Southwest
Cost(in cents)==> 14.9, 14.6, 11.9, 12.4
Suppose that, on a 3,000-mile New York to Los Angeles flight, United Continental, American, and Southwest flew a total of 235 empty seats, costing them a total of $99,060. If United Continental had three times as many empty seats as American, how many empty seats did each of these three airlines carry on its flight?
Click here to see answer by CPhill(1959) |
Question 1177662: The verbiage in this question is confusing me so much that I don't even know where to start. Any help in explaining and solving would be greatly appreciated.
The following table shows the amount spent by four U.S. airlines to fly one available seat 1 mile in the second quarter of 2014. Set up a system and then solve using technology.
// The table shows:
Airline ==> United Continental - American - Jet Blue - Southwest
Cost(in cents)==> 14.9, 14.6, 11.9, 12.4
Suppose that, on a 3,000-mile New York to Los Angeles flight, United Continental, American, and Southwest flew a total of 235 empty seats, costing them a total of $99,060. If United Continental had three times as many empty seats as American, how many empty seats did each of these three airlines carry on its flight?
Click here to see answer by ikleyn(52756)  |
Question 1177662: The verbiage in this question is confusing me so much that I don't even know where to start. Any help in explaining and solving would be greatly appreciated.
The following table shows the amount spent by four U.S. airlines to fly one available seat 1 mile in the second quarter of 2014. Set up a system and then solve using technology.
// The table shows:
Airline ==> United Continental - American - Jet Blue - Southwest
Cost(in cents)==> 14.9, 14.6, 11.9, 12.4
Suppose that, on a 3,000-mile New York to Los Angeles flight, United Continental, American, and Southwest flew a total of 235 empty seats, costing them a total of $99,060. If United Continental had three times as many empty seats as American, how many empty seats did each of these three airlines carry on its flight?
Click here to see answer by Edwin McCravy(20054)  |
Question 1175738: If point A = matrices 4 -4 -3 and B = 2 0 2 . Then find AB and BA
0 0 -2 2 -2 1
1 -4 -2 -1 -1 -2
I tried the following. I am not sure how to get the other numbers.
4x2 + -4x2 + -3x-1=3
0x0 + 0x-2 + -2x-1=-2
1x2 + -4x1 + -2x-2=2
Click here to see answer by CPhill(1959) |
Question 1169744: The general linear supply and demand for one-commodity market model are given by
P = aππ +b (a>0, b>0)
P = - cππ·+d (c>0, d>0)
a. Show that in matrix notation the equilibrium price, P, and quantity, Q satisfy.
[1 βπ] [π]=[π]
1 π π π
b. Solve this system to express P and Q in terms of a, b, c and d.
c. Write down the multiplier for Q due to changes in b and deduce that an increase in b lends to an decrease in Q.
Click here to see answer by CPhill(1959) |
Question 1168173: Lanre income from interest and wages is 4000 he double his investment and also get an increase to 6500 my what was his original income separately in both term (interest and wages). Using crammer rules.
Click here to see answer by CPhill(1959) |
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