Matrices and Linear Systems of Equations
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The augmented matrix of a linear system has been reduced by row operations to the form shown. In each case, continue the appropriate operations and describe the solution set of the original system.
1)
2)
Solve the system.
3)
4)
Determine if the system is consistent. Don not completely solve but explain your answer.
5)
Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system.
6)
Mark true or false and explain your answer.
a) every elementary row operation is reversible.
b) A 5x6 matrix has 6 rows.
c) The solution set of a linear system involving variables is a list of numbers ( ) that makes each equation in the system a true statement when the values are substituted for , respectively.
d) Two fundamental questions about a linear system involve existence and uniqueness.
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The augmented matrix of a linear system has been reduced by row operations to the form shown. In each case, continue the appropriate operations and describe the solution set of the original system.
1)
Solution. From the third row of this matrix , we can get a reduced equation which is
0=1
As 0=1 is impossible, we conclude that the original system has no solution.
2)
Solution. From the third row of this matrix , we can keep doing row operations to reduce it more. For instance, we use ½ to multiply the last row, so we have
Then we multiply the 4th row by 3 and add it onto the 3rd row, so we have
Then we multiply the 3rd row by 3 and add it onto the 2nd row, so we have
We add the 2nd row onto the first row to get
...
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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