Find a basis of the subspace of R^5 containing all that satisfy 5x_1+9x_2-40x_3=102x_4-76x_5=9x_2+30x_4-40x_5



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Posted on (Answer #1)

Let  basis of subspace of R^5 be   (x_1,x_2,x_3,x_4,x_5) such that




Let us write this in matrix form


write roe echlon form of the coefficient matrix


Thus basis of R^5={ (1,0,-8,-6,0),(0,1,0,-8,0),(0,0,0,0,1)}

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