TRUE-FALSE, Determine whether each statement below is either true of false. Write either TRUE or FALSE (all caps), as appropriate, before each one. a) ____ A linear system with a reduced row echelon form having a row of zeroes has no solutions. b) ____ No set of 6 dependent vectors in R^5 spans R^5. c) ____ Let V be a vector space and S be a subset of V. If V = span(S), then s is a basis for V. d) _____ If u middot v = 0 then either u = 0 or v = 0. e) _____ If v is a 5-component vector of norm 4, then ||3v|| = (3)^5 4 f) _____ The solution set of a consistent nonhomogeneous linear sysem Ax = b, where A is an m times n matrix and b is m times 1, is a subspace of R^n g) ____ A linear system with a reduced row echelon form having a row of zeroes has infinitely many solutions. h) _____ If u, v and w are all 5-component vectors then (u middot v) middot w = u middot (v middot w) h) ____ If u, v and w are all 5-component vectors then (u middot v) middot w = u middot (v middot w) i) ____ The general solution of the nonhomogeneous linear system Ax = b can be obtained by adding b to the general solution of the homogeneous linear system Ax = 0.

Show transcribed image text TRUE-FALSE, Determine whether each statement below is either true of false. Write either TRUE or FALSE (all caps), as appropriate, before each one. a) ____ A linear system with a reduced row echelon form having a row of zeroes has no solutions. b) ____ No set of 6 dependent vectors in R^5 spans R^5. c) ____ Let V be a vector space and S be a subset of V. If V = span(S), then s is a basis for V. d) _____ If u middot v = 0 then either u = 0 or v = 0. e) _____ If v is a 5-component vector of norm 4, then ||3v|| = (3)^5 4 f) _____ The solution set of a consistent nonhomogeneous linear sysem Ax = b, where A is an m times n matrix and b is m times 1, is a subspace of R^n g) ____ A linear system with a reduced row echelon form having a row of zeroes has infinitely many solutions. h) _____ If u, v and w are all 5-component vectors then (u middot v) middot w = u middot (v middot w) h) ____ If u, v and w are all 5-component vectors then (u middot v) middot w = u middot (v middot w) i) ____ The general solution of the nonhomogeneous linear system Ax = b can be obtained by adding b to the general solution of the homogeneous linear system Ax = 0.