In this problem we investigate Gaussian elimination of matrices with complex entries. Consider the following matrix...

 

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In this problem we investigate Gaussian elimination of matrices with complex entries. Consider the following matrix and vector 3i+1 4i 16 -5i-2 - B = 4i+1 4i - 20-6i-2 C = 2i 2i+1 5i - 12 -5i-3] i Method: If a matrix has complex entries, then Gaussian computation runs as in the case of real entries. In short, the only difference is that the arithmetic is carried out with complex numbers rather than real ones. (a) Use Gaussian elimination to solve the system exactly; that is, do not convert fractions or irrational numbers to decimals. Make sure to first find the row- echelon form (15 marks) of its augmented matrix and provide the general solution where the complex numbers are all in standard form (2 marks). (b) Compute the rank of B (2 marks). In this problem we investigate Gaussian elimination of matrices with complex entries. Consider the following matrix and vector 3i+1 4i 16 -5i-2 - B = 4i+1 4i - 20-6i-2 C = 2i 2i+1 5i - 12 -5i-3] i Method: If a matrix has complex entries, then Gaussian computation runs as in the case of real entries. In short, the only difference is that the arithmetic is carried out with complex numbers rather than real ones. (a) Use Gaussian elimination to solve the system exactly; that is, do not convert fractions or irrational numbers to decimals. Make sure to first find the row- echelon form (15 marks) of its augmented matrix and provide the general solution where the complex numbers are all in standard form (2 marks). (b) Compute the rank of B (2 marks).