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MATH Midterm One TF
Question | Answer |
---|---|
Is Every pair of lines in R^2 has an intersection? | False. |
Is Every 2 x 2 augmented matrix describes a system with either a unique solution or infinitely many solutions? | False. |
Does A matrix has infinitely many solutions exactly when the lines in the corresponding system are parallel? | False. |
Does Every matrix describe a system of equations? | Yes. |
A line L: ax+by=c contains (0,0) when c = 0. | Yes. |
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. |
If A=(aij) is a non augmented matrix and t is a real number then tA = (taij). | True. |
Any two matrices can be added. | False. |
A matrix (aij) is equal to a matrix (bij) if both matrices have the same size and for every j, aij = bij. | True. |
A matrix (aij) is equal to a matrix (bij) if both matrices have the same size and for every j, aij = bij. | True. |
For any two matrices A and B for which both AB and BA are defined, AB = BA. | False. |
If A and B are matrices for which AB and BA are defined then A and B have the same size. | False. |
For any two matrices A and B for which both AB and BA are defined, AB = BA. | False. |
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. |
If A and B are matrices for which AB and BA are defined then A and B have the same size. | False. |
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. |
If A is an n x n matrix and 0 is a n x n zero matrix then A + 0 = A = 0 +A. | True. |
If A is an n x n matrix then A has an inverse. | False. |
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. |
If A is an invertible matrix and X and Y are matrices for which AXA^-1 = AYA^-1 then X = Y. | True |