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2.(5 points)For whatcisc0cin Span101,1-12,c11,12-1?In other words, we’d like to see for whichcthere arex1, x2, x3, x4such that:x1101+x21-12+x3c11+x412-1=c0-cIn other words, the question is: for whichcis the following sys-tem consistent:x1+x2+cx3+x4=c-x2+x3+ 2x4= 0x1+ 2x2+x3-x4=-cLet’s find the row-echelon form of the augmented matrix:11c1c0-1120121-1-c
MATH 54-QUIZ 1-SOLUTIONS3Substracting the first row from the third, we get:11c1c0-1120011-c-2-2cAdding the second row to the third, we get:11c1c0-1120002-c0-2cBy the Fact discussed in section, this system has a solution ifand only if2-c6= 0(otherwise we’d have a row of the form0000?, where?6= 0), which givesc6= 2
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Math,Following,Row,RYAN TABRIZIAN,PEYAM RYAN TABRIZIAN