caex1 - MAS 3114 Test 1 1(10 pts Indicate whether the...

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MAS 3114 Test 1 1. (10 pts) Indicate whether the following are true or false: i.) If A and B are matrices such that AB is defined, then ( AB ) T = A T B T . T F ii.) If A and B are matrices such that AB is the n × n identity matrix, then BA is also an identity matrix. T F iii.) A system of simultaneous equations is consistent if the echelon form of the accompanying augmented matrix has at least one free variable. T F iv.) An n × n invertible matrix must always contain n pivots when placed in echelon form. T F v.) The echelon form of an augmented matrix of a system of linear, homogeneous equations must contain at least one free variable. T F vi.) A bijective mapping must always be surjective. T F vii.) If T is a transformation from R n to R m then there exists a matrix A such that T ( x ) = A x . T F viii.) Any set of five vectors in R 6 must be linearly independent. T F ix.) Let A be the augmented matrix for a simultaneous linear system of four equations and seven unknowns. The echelon form of A must contain at least two pivots. T F x.) Only n × n matrices have transposes.
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