Question

Testing for Linear Independence In Exercises 49-52, determine whether the set of vectors in M22 is linearly independent or linearly dependent. 32. A = (-; J.B-15 5C--817||

Answer 1

& 52 Testing vectors linearly for LI determine whether the set of in Maia in linearly dependent or independent. AL 3.6-63). Son I let W=&A, B, C set of objects. w is said to be LI if spans (W) Eo has only trivial solution and set of objects is said to be LD if spar (W) has non trivial sol. (Infinite son) Spans (W) = AX + B + C = 02x2 > 1-8 1-6 Oll-4-) 0 5J -310 178 9, OO -3 WA => [ 2*, }+puma -321 a lo 503) 7-673 1733/200) 1 +(-3% -100) (2x, 472-843 -2 -323 1 roog 1-341-643 , +54g +1743 / 7 0 27,-442-893 - 22 - 312 = 0 -3, -613=0 x + 50 2t 174320 WWWMWWWW

forry System of epu in Duo = D=12 -4 0-1 Matrix -8 1 - 3 -3) 0 - = y 2 - 3 1 0 5 17 J Number of variables 4 then Rank w D = Rank u LI then LD. if Rand < Number of variables & = using Echton form finding rank of D. 1 -2 -4 1 -2 -4) -21 -2 -4) - Rank (P) = 2 number of variables = 3 Rank DE 2 <3 w is 2D -

Its very eassy to understand no need to extra coments thanku.