Consider the following system of linear equations. x+z = 3, 2x+y+4x=5, -x+2y+3x=-5. (i) Write down the...

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Consider the following system of linear equations. x+z = 3, 2x+y+4x=5, -x+2y+3x=-5. (i) Write down the augmented matrix of this system. (ii) Use elementary row operations to bring the augmented matrix into reduced row echelon form. Show your steps and, at each step, say what elementary row operations you are performing. (iii) Write down all the solutions of the linear system in vector form. Consider the following system of linear equations. x+z = 3, 2x+y+4x=5, -x+2y+3x=-5. (i) Write down the augmented matrix of this system. (ii) Use elementary row operations to bring the augmented matrix into reduced row echelon form. Show your steps and, at each step, say what elementary row operations you are performing. (iii) Write down all the solutions of the linear system in vector form.