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MATH Midterm One TF

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Question
Answer
Is Every pair of lines in R^2 has an intersection?   False.  
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Is Every 2 x 2 augmented matrix describes a system with either a unique solution or infinitely many solutions?   False.  
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Does A matrix has infinitely many solutions exactly when the lines in the corresponding system are parallel?   False.  
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Does Every matrix describe a system of equations?   Yes.  
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A line L: ax+by=c contains (0,0) when c = 0.   Yes.  
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If ax+by is less than or equal to c, we can sketch the inequality by drawing the line L: ax+by=c and then shade below L.   True.  
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If A=(aij) is a non augmented matrix and t is a real number then tA = (taij).   True.  
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Any two matrices can be added.   False.  
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A matrix (aij) is equal to a matrix (bij) if both matrices have the same size and for every j, aij = bij.   True.  
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A matrix (aij) is equal to a matrix (bij) if both matrices have the same size and for every j, aij = bij.   True.  
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For any two matrices A and B for which both AB and BA are defined, AB = BA.   False.  
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If A and B are matrices for which AB and BA are defined then A and B have the same size.   False.  
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For any two matrices A and B for which both AB and BA are defined, AB = BA.   False.  
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If A is an m x n matrix and if B is an n x p matrix, and p does not equal m, is the matrix multiplication AB defined?   True.  
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If A and B are matrices for which AB and BA are defined then A and B have the same size.   False.  
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If A is an m x n matrix and if B is an n x p matrix, and p does not equal m, is the matrix multiplication AB defined?   True.  
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If A is an n x n matrix and 0 is a n x n zero matrix then A + 0 = A = 0 +A.   True.  
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If A is an n x n matrix then A has an inverse.   False.  
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If A is an invertible matrix then it is possible for A to have two inverses B and C, and B does not equal C.   False.  
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If A is an invertible matrix and X and Y are matrices for which AXA^-1 = AYA^-1 then X = Y.   True  
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