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(b)
\The given system of equations are
\x1 - x2 - 7x3 + 7x4 = 5
\-x1 + x2 + 8x3 - 5x4 = -7
\3x1 - 2x2 - 17x3 + 13x4 = 14
\0 x1 - 0 x2 - 0 x3 + 0 x4 = 0
\We can write above equations are in matrix form as
\
R indicates Rows
\C indicates Columns
\R2 = R2+R1
\R3 = R3-3R1
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Interchange R3 with R2
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We can write above matrix is in equations form as
\x1 - x2 - 7x3 + 7x4 = 5 ----------------------------(1)
\x2 + 4x3 - 8x4 = -1 ---------------------------(2)
\x3 + 2x4 = -2 ---------------------------(3)
\Let x4 = k
\Substitute x4 = k in equation (3)
\x3 + 2(k) = -2
\x3 = -2 - 2k
\Substitute x4 = k and x3 = -2 - 2k in equation (2)
\x2 + 4(-2 - 2k) - 8(k) = -1
\x2 = -1 + 8k + 8k + 8
\x2 = 7 + 16k
\Substitute x2 = 7+16k , x4 = k and x3 = -2 + 2k in equation (1)
\x1 - (7+16k) - 7(-2 + 2k) + 7(k) = 5
\x1 = 5 + 7 +16k + 14 - 7k + 14k
\x1 = 26 + 23k
\Solution :
\x1 = 26+23k
\x2 = 7+16k
\x3 = -2 - 2k
\x4 = k