Questions on Algebra: Matrices, determinant, Cramer rule answered by real tutors!

Tutors Answer Your Questions about Matrices-and-determiminant (FREE)

Question 80919: If p, q, and r are positive integeres and the following is true p + 1/(q + 1/r) = 25/19, then find q.

Click here to see answer by ankor@dixie-net.com(15634)

Question 81905: Solve the system using an augmented matrix. Show you work
5x + 4y - z = 1
2x - 2y + z = 1
-x - y + z = 2
Click here to see answer by Edwin McCravy(8881)

Question 82428: Solve each matrix equation for X
1 0 0
0 1 0
0 0 1 X
= 4
-5
3
Click here to see answer by jim_thompson5910(28503)

Question 82431: 0 0 2
0 0 1 X
1 1 1
=
3
4
3
Click here to see answer by stanbon(57239)

Question 82427: 1 1
1 -1 X
= 3
-1
Click here to see answer by stanbon(57239)

Question 82426: Solve each matrix for equation for X
1 2
1 -2 X =
2
-2
Click here to see answer by stanbon(57239)

Question 82714: Use Cramer's rule to solve. If inconsistent or dependent, so state.
11x + 3y = 1
5x + 2y = 4
Click here to see answer by stanbon(57239)

Question 82718: Evaluate the determinant
6 5 6
1 1 3
2 5 1
Click here to see answer by stanbon(57239)

Question 83015: Please help. I have been working this problem for three days and keep getting different answers. My downfall is the signs, I think.
Use Cramer's Rule to solve the linear system
4x + 3y - z = 12
x - 3y + 3z = 14
3x + y + z = 18
I know that D = 4 3 -1
1 -3 3
3 1 1
Dx= 12 3 -1
14 -3 3
18 1 1
Dy= 4 12 -1
1 14 3
3 18 1
I understand how to proceed but the signs are giving me a headache. I am at the point that I just want to view the right answer in its entirity to see where I am going wrong. Thanks in advance.
Click here to see answer by scott8148(6628)

Question 83031: EVALUATE THE DETERMINANT OF THE MATRIX
(6 2) THE ANSWER I GOT WAS -18+-2=-20
(-1 -3) But the answer the teacher gave me was 18+2=-16
and I was wondering how is that not negative and could you please explain to me what exactly is a determinant.
Click here to see answer by bucky(2189)

Question 83333: I have been working on this for days. If anyone can help, I would appreciate it. I have to show all of my work.
Solve using addition, Cramers Rule or matrix.
2x + y - 3z + 4s + t = -2
3x + 2 y - 2z - s + 2t = 7
x - y + z - 2s - 2t = 0
-x - 2y - z + 2s + t = 5
2x + 2y - 2z +s + 2t = 3

Click here to see answer by jim_thompson5910(28503)

Question 83370: WHAT IS THE DEFINITION OF MATHEMATICAL COMPUTATION?
Click here to see answer by mathman409(67)

Question 83881: Hi, Please help me with this one:
If , which of the following must be true? The exponent is actually 1/2 (not .5), I just didn't know how to input it using the plot formula. The answer is but I don't know why. Thanks!
Click here to see answer by stanbon(57239)

Question 83994: can someone help me pleae step by step.
use the gauss-jordan method to solve
4x-3y+z+w = 21
-2x-y+2z+7w = 2
10x- 5z-20w = 15
Click here to see answer by stanbon(57239)

Question 83993: can someone help me please......
use the gauss-jordan method to solve each system of equations.
x + 3y -6z = 7
2x -y +2z = 0
x + y +2z = -1
Click here to see answer by stanbon(57239)

Question 84137: I am having trouble finding the determinant of the matrix [-1 2] [1 3] with the 1 and 3 directly under the -1 and 2, with one set of []. Any help is greatly appreciated.
Thank you!

Click here to see answer by venugopalramana(3286)

Question 84338: The following matrix is a reduced augmented matrix obtained from a system of equations. The system has ______ solutions?
1 0 0 3 6
0 1 0 5 4
0 0 0 0 -2
0 0 0 0 0

A. None
B. One
C. Two
D. infinite
Click here to see answer by jim_thompson5910(28503)

Question 84386: find the inverse, if it exists,in the matrix. I am not sure and don't understand how to do the inverse. I used the underscore to separate the numbers within the matrix.
2_ 0_ 4
3_ 1_ 5
-1_1_-2
Click here to see answer by venugopalramana(3286)

Question 84358: Can someone help me with these two problems explaining them to me if someone has time please.
Problem #1
If A is a 5 X 2 matrix and A + k = A, what do you know about K?

Problem #2
Find the values of the variables in each equation.
i don't know how to do the matrix box so i will separate them the first matrix is a 2 X 3 plus the second matrix that is a 2X 3 Equal the third matrix which is a 2 X 3. I try to separate the numbers inside the matrix with a forward slash. so a+2 is ontop of row that reads 4k and then the same for the second matrix and the last matrix
[ a+ 2 / 3z+1 / 5m ] + [ 3a / 2z / 5m] = [ 10 / -14 / 80]
[ 4k / 0 / 3 ] [ 2k/ 5 / 6] [ 10 / 5 / 9]
Click here to see answer by IamaangelXxX(5)

Question 84472: [1 -1 0]
[0 1 1]
[1 0 -1]
What is the inverse of this matrix?
Click here to see answer by venugopalramana(3286)

Question 84469: the following matrix is a reduced augmented matrix obtained from a system of equations. The system has ____ solutions?

1 0 3 -5 |7
0 1 -2 0 |4
0 0 0 0 |0
0 0 0 0 |0

A. One
B. Two
C. Infinite
D. No

Click here to see answer by venugopalramana(3286)

Question 84471: A = , B =
FIND A - 2B
Click here to see answer by Edwin McCravy(8881)

Question 84506: For the input-output matrix A, and the output matrix X, of three industries, find the amounts consumed internally by the production process.

[0.10 0.15 0.10]
[0.20 0.05 0.08]
[0.04 0.06 0.02] = A

[500]
[800]
[400] = X

Click here to see answer by vertciel(183)

Question 84623: [1 5][4 -2]
[-2 3][0 1]=
I imagine this is a case of multiplying the 2 matrixs? Please assist me with a solution and how it was obtained
Click here to see answer by jim_thompson5910(28503)

Question 85467: Evaluate matrix equation
(1 5) (1 2)
(2, 3)(0 1)
Click here to see answer by jim_thompson5910(28503)

Question 86663: Mike, Joe, and Bill are painting a fence. The painting can be finished if MIke and JOe work together for 4 horus and Bill works alone for 2 hours, or if Mike and Joe work together for 2 horus and Bill works alone for 5 hours, or if MIke works alone for 6 hours, Joe works alone for 2 hours, and Billw orks alone for 1 hour. how much time would it take each man to paint the entire fence by himself?
Click here to see answer by ankor@dixie-net.com(15634)

Question 87180: the following matrix is obtained from the augmented matrix of a system of equations.

[1 0 3 | 20]
[0 1 2 | -2]
[0 0 1 | 4] The solution to the system is

A. No solution
B. (20, -2, 4)
C. (3,2,1)
D. (8, -10,4)
Click here to see answer by stanbon(57239)

Question 87179: the augmented matrix
[1 3 2 | 4]
[2 -1 5 | -2]
[-3 1 6 | 1]

represents what system of equations.

Click here to see answer by stanbon(57239)

Question 87883: A square matrix A is idempotent if A^2 = A.

a) Show that if A is idempotent, then so is I - A.

b) Show that if A is idempotent, then 2A - I is invertible and is its own inverse.
Click here to see answer by kev82(148)

Question 87893: how do you find the determinant of a 4 by 4 matrix?
Click here to see answer by stanbon(57239)

Question 88570: Find the center, the vertices, and the foci of the ellipse with the given equation. Then draw the graph.

(x+3)squared, over 25 + (y-5)squared, over 36 =1

Click here to see answer by stanbon(57239)

Question 89489: PLEASE HELP ME!!!!
I need help because i am confused i am not getting this please explain these two problems step by step so i can refocuse on what i have to do....If someone has afew thank i really appreciate all your help...
Problem #1
(*I used the underscore to separate the numbers*)
find the inverse, if it exists, for the matrix
-2_1_3
3_-1_2
-4_2_0

Problem #2
Solve the matrix equation AX=B for X by finding A to power
* Matrix A is a 3X3
A =
2_-1_3
-3_4_-5
-4_0_6
and matrix b is a 3X1 B=
9
6
-9
Click here to see answer by stanbon(57239)

Question 89933: .813x+.743y=.079
.491x+.114y=.826
solve by substitution, graphing, manipulating coefficients, and cramer's rule, i cant figure out what to do because all the variables have numbers?????
Click here to see answer by stanbon(57239)

Question 93270: Many college graduates who are employed full-
time have longer than 40-hour work weeks. Suppose that we wish to estimate the mean number of hours
, , worked per week by college graduates employed full-time. We'll choose a random sample of college
graduates employed full-time and use the mean of this sample to estimate . Assuming that the
standard deviation of the number of hours worked by college graduates is 6.00 hours per week,
what is the minimum sample size needed in order for us to be 95%confident that our estimate is
within 1.2 hours per week of ?

Click here to see answer by stanbon(57239)

Question 93551: how can i know just by looking at any two matrices if their product is commutative?
Click here to see answer by stanbon(57239)

Question 93397: ) Is it always possible using the elementary row operations for matrices to transform any square matrix into echelon form with all 1's along its main diagonal?
2) Can you take any two matrices and add them, subtract them and multiply them together?
3) Is it possible to divide two matrices?

Click here to see answer by stanbon(57239)

Question 93405: Represent the given matrix with a system of equations in x, y, and z
-2 3 1 line 5

1 0 3 line -6
4 9 0 line 13

I am not sure how to show this the way that shows in my book when I write line it is a verticle line that goes all the way down
Click here to see answer by stanbon(57239)

Question 93647: FOR PROBLEMS 18 - 20 USE THESE MATRICES:
A = [2 1 7
4 3 8
6 5 9]

B = 0
2
3
Find A2,1

If C = AxB, the order of C is:

If C=AxB, find C2,1.

Thank you in advance for your help - these are so tough for me
Click here to see answer by jayanthihemkos@yahoo.com(87)

Question 93645: Given A = [3 -2] and
[1 4]

B = [-1 2] , find A + B .
[-3 5]
This is hard to set uo because it is not 3-2 it is 3 and neg 2 so on
Thank you for your help
Click here to see answer by jayanthihemkos@yahoo.com(87)

Question 94014: When finding the product,
-2 0 1
4 3 2
-1 5 0
and
-1 4 -2
0 -1 3
-2 0 -5
how many pairs of numbers must be multiplied together?

1. What is a square matrix?
2. What is meant when a matrix is said to have dimensions "b" by "a"?
3. Under what conditions can two matrices be added?
4. What conditions are necessary in order to be able to multiply two matrices?
I am so desperate for help I am willing to pay you I just need someone to help me- PLEASE!!!!!!!!
Click here to see answer by stanbon(57239)

Question 94176: 1. Write the augmented matrix for the given system:
x + y + 2z = 6
3x + 2y + z = 9
x - y = 4
2. Use the system in problem #1. Without
interchanging any of the rows in the augmented
matrix, what is the first value which will be
replaced with zero when using the Gaussian
Elimination method?

Click here to see answer by Edwin McCravy(8881)

Question 94292: Given these matrices and their dimensions: A 3x2, B 3x2, and C 2x4 Which of the following can NOT be performed?
Click here to see answer by jayanthihemkos@yahoo.com(87)

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