# Matrices : Row Operations and Echelon Form

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1) An augmented matrix of a linear system has been reduced by row operations to the following form. Continue the appropriate row operations and describe the solution set of the original system.

Please show every step no matter how minor, use the brackets for each reduction and write out every equation change. Please leave no details out. Thanks!

1 -2 0 3 -2

0 1 0 -4 7

0 0 1 0 6

0 0 0 1 -3

2) Solve the given augmented system.

Please show every step no matter how minor, use the brackets for each reduction and write out every equation change. Please leave no details out. Thanks!

1 -3 4 -4

3 -7 7 -8

-4 6 -1 7

3) Determine the value of h such that the matrix is the augmented matrix of a consistent linear system.

Please show every step no matter how minor, use the brackets for each reduction and write out every equation change. Please leave no details out. Thanks!

a)h is just a variable right?

b)What does it mean a consistent linear system?

c) 1 h -3

-2 4 6

4) Row reduce the given matrix to educed echelon form. Circle the pivot positions in the final matrix and in the original matrix, and list the pivot columns.

Please show every step no matter how minor, use the brackets for each reduction and write out every equation change. Please leave no details out. Thanks!

1 3 5 7

3 5 7 9

5 7 9 1

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Matrix Row Operations and Echelon Form are investigated. The solution is detailed and well presented.

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1) An augmented matrix of a linear system has been reduced by row operations to the following form. Continue the appropriate row operations and describe the solution set of the original system.

1 -2 0 3 -2

0 1 0 -4 7

0 0 1 0 6

0 0 0 1 -3

Solution. We use r2+4*r4 to denote an operation: the 4th row times 4, then add on the second row. We get

1 -2 0 3 -2

0 1 0 0 -5

0 0 1 0 6

0 0 0 1 -3 ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

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- "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."
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