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SiddharthThakur
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 Mar 23, 2013
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Question
a) For each of the following matrices explain why the matrix is not invertible.
i)[2,0,0_0,0,0_9,3,0]
ii)[3,4,6_7,2,1_6,812]
iii)[5,2,15_1,4,3_2,1,6]
b) Suppose A is an n×n matrix with the property that the equation Ax = 0 has only the trivial
solution. Without using the Invertible Matrix Theorem, explain directly why the equation
Ax = b must have a solution for each b in Rⁿ
a) For each of the following matrices explain why the matrix is not invertible.
i)[2,0,0_0,0,0_9,3,0]
ii)[3,4,6_7,2,1_6,812]
iii)[5,2,15_1,4,3_2,1,6]
b) Suppose A is an n×n matrix with the property that the equation Ax = 0 has only the trivial
solution. Without using the Invertible Matrix Theorem, explain directly why the equation
Ax = b must have a solution for each b in Rⁿ
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