Solution

In[86]:=

(*a*)LinearSolve[{{1, 1}, {1, -1}}, {1, -1}]

Out[86]=

{0, 1}

In[87]:=

(*b*)LinearSolve[{{1, 2, 10}, {10, 2, 10}, {1, 2, 3}}, {10, 1, 0}]

Out[87]=

{-1, -23/14, 10/7}

In[88]:=

(*c*)LinearSolve[{{1, 2, 3}, {0, 1, 2}, {0, 0, 1}}, {1, 1, 1}]

Out[88]=

{0, -1, 1}

In[89]:=

(*d*)M = {{1, 1, 1}, {1, 0, -1}, {2, 1, 0}} ; LinearSolve[M, {0, 1, 2}] Det[M]

LinearSolve :: nosol : Linear equation encountered which has no solution.  More…

Out[90]=

LinearSolve[{{1, 1, 1}, {1, 0, -1}, {2, 1, 0}}, {0, 1, 2}]

Out[91]=

0

The last set of equations has no solutions because the determinant of the matrix of coefficients is zero.


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