Question

For the following questions, consider the matrix: ſi 0 21 0 1 0 A= 1 -1 2 0 1 0 1 Please circle the correct answer in parts (a.)-(e.). (a.) The rank of A is 1 2 3 4 (b.) Any basis for the range space of A, R(A), will consist of how many vectors? 1 2 3 4 (c.) The dimension of the null space of A, dim(N(A)) is: 0 1 2 3 (d.) The following vector is in the null space of A (circle all that apply): 3 21 w = 0 = - 6 y = 0 = 1 0.5 3 L- 1 1 -1 (e.) A basis for R(A) is given by the following set of vectors (circle all that apply): [1 0 2], ) · (iii) { [0 1 0], } 11 -1 2] li -11 1

Answer 1

Solution get we will A ' fated Of a) Jhank echelon foro.. asing show sieduced R₂ R₂ + R2 ооо ooo R2 Ru - Ra . Rank of (A) = (6). Here Pank of A = Q => Basis of RCA) will A a je consist orange space of A @ vectors vectos CONSIS with cs Scanned with Answer @ CamScanner

(C) n = dim (ganac Space Of A) dim ( bull space' of AJ : clim (null Space Of A) - A-diers (Grange space of A) = 3472 9 va R3 - R" dg() WCH)= 3 Answe Here null Space is and 1 0 BP], 7 - Because Row space is [oa] and coro] and ! Trion] - [10] Hence the Cs Scanned with CamScanner answer.