Let A be 3 × 3 matrix with det(A)=3. (a) What is the reduced row echelon form to which A is row equivalent? (b) How many solutions does the homogeneous system Ax = 0 have?
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Let Ax = b be a linear system whose augmented matrix (A|b) has reduced row echelon form $$ \left(\begin{array}{ccccc|c}{1} & {2} & {0} & {3} & {1} & {-2} \\ {0} & {0} & {1} & {2} & {4} & {5} \\ {0} & {0} & {0} & {0} & {0} & {0} \\ {0} & {0} & {0} & {0} & {0} & {0}\end{array}\right) $$ (a) Find all solutions to the system. (b) If $$ \mathbf{a}_{1}=\left(\begin{array}{l}{1} \\ {1} \\ {3} \\ {4}\end{array}\right) \quad \text { and } \quad \mathbf{a}_{3}=\left(\begin{array}{r}{2} \\ {-1} \\ {1} \\ {3}\end{array}\right) $$ determine b.
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