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# Matlab to solve numerical linear algebra LU-decomposition

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Use Matlab commands lu(A) and A b to solve the following problem. I need the answer as a matlab file, or at least as a copy of the print-out of the input and output lines.

Let

2 2 -4 10
A = 1 1 5 b = -2
1 3 6 -5

( A is 3 x 3 matrix and b is a vector)

1). Use Gaussian elimination with partial pivoting to find matrices L and U such that U is upper triangular, L is lower triangular with | l_ij| =< 1 for all i > j and LU = A', where A' can be obtained from A by interchanging rows.

2). Use LU decomposition to solve Ax = b

##### Solution Summary

This provides a Matlab file to solve given Gaussian elimination and LU decomposition problems.

Solution provided by:
###### 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!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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