Find an LU factorization of the following matrices а. 1 4 -1 7 -2 1 -4 6 –1 -2 -3 1 -1 7 Determine the column vectors of (a) are linearly independent or not by using the information obtained after making LU factorization.

What exactly is meant by "span of column vectors", what is meant by column vector?  How would you solve this problem?

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Given the matrix A = 0 2 2 0 2 2 find an orthogonal diagonalization of A: A = QDQ" Enter each matrix Q and D in the format [[a11 , a12 , a13] , [a21 , a22 , a23] , [a31, a32, a33]]. Note: if you need to enter a square root of a number x you can do it as follows: sqrt (x). Alternatively, you can compute matrix entries in the decimal form rounded to 3 decimal places, and enter them in this. Matrix Q: Matrix D: