5. True or False. You must explain the reason for your answer.a: If a matrixMis invertible, then kernel ofMis just the zero vector.b: Ifu, v, w2V,VasubspaceofRn, then the vector 2u-3v+4wis also an elementofV.c: If a 5 by 5 matrixAhas rank 5,then any linear system of equations with coefcientmatrixAwill have a unique solution.d: There exists a 2⇥2matrixBso thatB✓11◆=✓12◆,andB✓22◆=✓21◆.e: LetAbe a matrix of size 3⇥5. Assume that the equationAx=0@1241Ahas a solution. Then it has in±nitely many solutions.
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This note was uploaded on 11/22/2011 for the course MATH 235 taught by Professor Markman during the Fall '08 term at UMass (Amherst).