select only one option 5 Determine which of the following is

**select only one option

5. Determine which of the following is FALSE. a. Let A be a 2 x 3 matrix. If Ax = b is consistent, then there are infinitely many solutions. b. The equation Ax = b is consistent if A has a pivot position in every row. e. If A = [a1 a2] ? a1 + 4a2 = b. Then A [ ] = b d. If Au = 0 and Av = 0, then for any w epsilon Spam{u, v}, Aw = 0. e. none of these.

Solution

(a)= TRUE

Because 2x3 matrix means 2 row and 3 columns and hence 2 equations and 3 variables. number of variables are more than number of equations hence there will be infinitely many solutions.

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(b) = FALSE

Because It may be that there is no pivot in 2nd row, then also answer can be infinitely many solutions.

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(c) TRUE

it is just representations of equation into matrix form.

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(d) TRUE

we can break given w is span {u,v} so w=au+bv

Aw=A(au+bv)=A(au)+A(bv)=a(Au)+b(Av)=a*0+b*0=0

hence Aw-0