homework on Cramer s rule Solution: First we shall write system of linear equations in matrix form 3x+4y+z=0 4x-y+z=8 3x+5y+4z=0 in matrix form, \[A=\left[\begin{matrix}3&4&1\\4&-1&1\\3&5&4\\\end{matrix}\right],\ B=\left[\begin{matrix}0\\8\\7\\\end{matrix}\right],\ X=?\] First we shall find determinant of A \[\left|A\right|=\left|\begin{matrix}3&4&1\\4&-1&1\\3&5&4\\\end{matrix}\right|\] \[=3\left(-4-5\right)-4\left(16-3\right)+1\left(20+3\right)\] \[\left|A\right|=-56\] \[{|A}_x|\ =\left|\begin{matrix}0&4&1\\8&-1&1\\7&5&4\\\end{matrix}\right|=-53\] \[\left|A_y\right|=\left|\begin{matrix}3&0&1\\4&8&1\\3&7&4\\\end{matrix}\right|=79\] \[\left|A_z\right|=\left|\begin{matrix}3&4&0\\4&-1&8\\3&5&7\\\end{matrix}\right|=157\]…
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