TRUEFALSE Determine whether each statement below is either t

TRUE-FALSE, Determine whether each statement below is either true or false. Write either TRUE or FALSE (all caps), as appropriate, before each one. _______A linear system with a reduced row echelon form having a row of zeroes has no solutions. ________No set of 6 dependent vectors in R^5 spans R^5. ________Let V be a vector space and S be a subset of V. If V = span(S), then S is a basis for V. __________If u. v = 0 then either u = 0 or v = 0. If v is a 5-component vector of norm 4, then || 3v || = (3)^5 4 The solution set of a consistent nonhomogeneous linear system Ax = b, where A is an m times n matrix and b is m Times 1, is a subspace of R^n ______A homogeneous linear system with a square coefficient matrix and reduced row echelon form having a row of zeroes has infinitely many solutions. If u, v and w are all 4-componcnt vectors then (u*v)*w = u*(v*w) _____ 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.

Solution

Note that --\'. No solution means only trivial solution.

And Rx=0 have only trivial solution iff R is identity matrix

a) is not true

Given that a row of R is zero which imples that R is not identity and hence Rx=0 will not have only trivial solution that means Rx=0 wl have solution and this means that system will have solution.

B) is true . set of 6 dependent vectors in R5 may be span R5

Set bassis of R5 and include one extra vector

C) V vdctor space and S is subset of V V= span(S) then it is not necessery that S is basis as S maybe linearly dependent subset of V

D) u.v=0 then either u=0 or v=0

Not true ,as u=(1,2) and v =(1,-1/2) belongs to R2

u.v= (1)(1)+(2)(-1/2)=1-1=0