Question

1 -3 -2 -5 -14 -6-3-8 -21 2 8.(15 pts. total) M= is row equivalent to -2 6 1 4 5 -9 -2-7 -14 + (1-3 0-1 0 0 0 2 7 2 Pivels L 0 0 0 0 0 0 0 0 0 0 (a) Find k and/ so that Nul Mc R and Col Mc R (b) Without calculations, list rank M and dim Nul M. (c) Find bases for Col M and Nul M. (Hint: Use L to solve Mx= 0.) Hint: No row operations are required for this problem.

if whoever answers this could be detailed with explanations please!

Answer 1

M ů a 4X Į matrix. So, Pt ore presents a kinean tolaus formatum from pa → R4 M:Rox R4 a) Nur(M) a domain NalueRa CK COL (M) e Codomain colens e R4 (9 = 4) b) Rank (M) = No of Non zeve rows = 2 din NUL(M) =_NO_OfGolemm - Rank - 5 -2 = 3 c) Base for Col(M)= B = {(1,0,0,0), (0,1,0,0) Columus that have pivot elements, encircled) - d) To find the basis for th Nul (M) het X=(x, y, z, u, w & NULLM) OLM XEO > ool27 ooooo loooooo Liu 6f Nost poloob

t- 34 دلا = 0 = 0 - 29 -3 = = -2-700 = 7 +20 + 9 = (ق ,u ,ی-20ی لارا +3) = (فارuر92 ملاع = X 1 (ہرا ,3 ,2 ,1) W + زه ره ره را,3) 4- کاره - ره رو) 08 + ابهررهرهرهرلر2-رهرلكررهرهرهرل,3 for Nul (M) = BI Basis