Determine if b is a linear combination of a1,a2, and a3. a1=[1−20], a2=[012], a3=[5−68], b=[2−16]

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Determine if b is a linear combination of a1,a2, and a3. a1=[1−20], a2=[012], a3=[5−68], b=[2−16]

Fatema Sutton · Accepted Answer

We must ascertain whetherb=[2−16]is a linear combination of&amp;nbsp;a1,a2&amp;nbsp;and&amp;nbsp;a3a1=[1−20],&amp;nbsp;a2=[012]&amp;nbsp;and&amp;nbsp;a3=[5−68]From equation we need to determine whether weights&amp;nbsp;x1,x2&amp;nbsp;and&amp;nbsp;x3&amp;nbsp;exist such thatx1a1+x2a2+x3a3=bConsiderx1[2−20]+x2[012]+x3[5−68]=[2−16][x1−2x10]+[0x22x2]+[5x3−6x38x3]=[2−16][x1+5x3−2x1+x2−6x32x2+8x3]=[2−16]Thus, the equation system is obtainedx1+5x3=2−2x1+x2−6x3=−12x2+8x3=6Isolate&amp;nbsp;x1=2−5x3&amp;nbsp;for&amp;nbsp;x1+5x3=2&amp;nbsp;then substitute in&amp;nbsp;−2x1+x2−6x3=−1&amp;nbsp;to get−2(2−5x3)+x2−6x3=−14x3+x2−4=−1Isolate&amp;nbsp;x2=3−4x3&amp;nbsp;for&amp;nbsp;2x2+8x3&amp;nbsp;then substitute in&amp;nbsp;4x3+x2=−14x3+3−4x3−4=−1.Expressing&amp;nbsp;x1&amp;nbsp;in terms of

Determine if b is a linear combination of a_1,a_2, and a_3.

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