Let γ={t2−t+1,t+1,t2+1}andβ={t2+t+4,4t2−3t+2,2t2+3}beorderedbasesforP2(R). Find the change of coordinate matrix Q that changes β coordinates into γ− coordinates
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Let t2+t+4=γ1(t2−t+1)+γ2(t=1)+γ3(t2+1) ⇒γ1+γ3=1,−γ1+γ2=1,γ1+γ2+γ3=4 ⇒1+γ2=4 ⇒γ2=3 −γ1+γ2=1⇒−γ1+3=1⇒γ1=2 γ1+γ3=1⇒2+γ3=1⇒γ3=−1 Let 4t2−3r+2=γ1(t2−t+1)+γ2(t+1)+γ3(t2+1) ⇒γ1+γ3=4,−γ1+γ2=−3,γ1+γ2+γ3=2 ⇒4+γ2=2 ⇒γ2=−2 −γ1+γ2=−3⇒−γ1−2=−3⇒γ1=1 γ1+γ3=4⇒1+γ3=4⇒γ3=3 Let 2t2+3=γ1(t2−t+1)+γ2(t+1)+γ3(t2+1) ⇒γ1+γ3=2,−γ1+γ2=0,γ1+γ2+γ3=3 ⇒2+γ2=3 ⇒γ2=1 −γ1+γ2=0⇒−γ1+1=0Ri>↔owγ1=1 γ1+γ3=2⇒1+γ3=2⇒γ3=1 Not exactly what you’re looking for? Ask My Question This is helpful 84
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The system of equation {2x+y=14x+2y=3 by graphing method and if the system has no solution then the solution is inconsistent. Given: The linear equations is {2x+y=14x+2y=3
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