SIT292 - Systems of Linear Equations - Eigenvalues and Similarity - Matrix - Data Analytics Assessment Answer

Assessment Task:

SIT292 - Systems of Linear Equations Data Analytics Assessment Answer

Task

Consider the following system of linear equations and answer the subsequent questions

x1+ x2+ x3− x4 = −2

3x1 +4x3+ x4 = 10

x1+2x2 −2x4 = −3

x2− x3+2x4 = 7

(a) Write the system as Ax = b for some matrix A and a vector b 
(b) Compute the rank of A 
(c) Decide if the system has a unique solution, infinitely many solutions or no solution (1 point). Justify your answer
(d) Does the matrix A have an inverse? Give an answer

(e) Use Gaussian elimination to solve the system. Make sure to first find the row-echelon form of its augmented matrix and provide the general solution

Part (a) The possible marks are 0, 0.5 and 1, and they have the following meaning.
0: No matrix A or vector b is provided.
0.5: Either A or b is provided.
1: Both A and b are provided.
—
Part (b) The possible marks are 0, 1 and 2, and they have the following meaning.
0: The rank is not computed.
1: There are mistakes in the computation, but the procedure is correct.
2: The rank is computed correctly.
—
Parts (c) and (d) The possible marks are 0, 1 and 2, and they have the following meaning.
0: Either no answer is provided or both the answer and the justification are incorrect.
1: A correct answer is provided but the justification is incorrect, or vice versa.
2: Both the answer and the justification are correct.
—
Part (e) The possible marks are 0, 1, 2 and 3, and they have the following meaning.
0: No row-echelon form matrix is provided or solution is provided.
1: There are problems in the computation of the row-echelon form matrix, but the procedure is mostly correct.
2: The row-echelon form matrix is correct, but the solution has mistakes.
3: Both the row-echelon form matrix and the solution are correct.

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