Quiz 5 with Solutions | Applied Linear Algebra | MATH 415, Quizzes of Linear Algebra

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Math 415 - Section D1 Quiz V SOLU TIoMs No calculators or other electronic devices may be used. Show all work, have fun, and good luck! (10 points possible) Name: Problem 1. (3 points) Find the dimension of (i) the column space and (ii) the left null space of the matrix 1 -3 0 -[; —4 ; 0 -5 -5 Reon A. OT Born Be [-30 L-30 1-30 {-30 1-30 130) | act? ete Oo 22 2742 o2Z2l foal | o7ss ess /~|9e° O -S5 JW| Oo -5-S oof] | a1 42 ore ' -14f Oo vt eo} chim C(A)= rank (A) =3 | Am CCA)s neni (A)=2 chim v(a") = 4 - rank (4) =f. aim N(A*)= 4 -rank(A)=2 Problem 2. (2 points) Describe the four subspaces for the matrix A= (3 we) Peat Reonfs R(A)= spf (3,2 ROA)= span (43 CCA)= spang (3) 2 CCA)= spent C¥)§ N(A)= spon § (2) 8 N(A)espu3 (7 )8 N (AT =spe0§ (2)3 Meary>see§ (1)§ (OVER)