ࡱ> *,)fy bjbj 9A{{ ,,,@@@@Dd@0".~fff|!!!!!!!^#&!,7|!f|!ccc:8f,|!c!cc: ,O!|or< !"00" R&o&O!&,O!pc!!i0"& : College Algebra Reduced Row Echelon Form (RREF) Name__________________ From the augmented matrix given, determine whether the system is consistent and independent, consistent and dependent, or inconsistent. Give solution if possible, and if dependent, give family of solutions.  EMBED Equation.BREE4  2.  EMBED Equation.BREE4  3.  EMBED Equation.BREE4  Solve each system of equations by using the augmented matrix method. Determine whether the system is consistent and independent, consistent and dependent, or inconsistent. If dependent, give family of solutions.4.  EMBED Equation  5.  EMBED Equation 6.  EMBED Equation 7.  EMBED Equation  8.  EMBED Equation 9.  EMBED Equation 10.  EMBED Equation  11.  EMBED Equation 12.  EMBED Equation 13.  EMBED Equation  14.  EMBED Equation 15.  EMBED Equation Write the system of equations represented by each matrix. Do not solve.16.  EMBED Equation  Solving Systems of Equations with Reduced Row Echelon Form command Vocabulary Augmented Matrix: the coefficient matrix with added column(s) Example: Solve 2x + 3y z = 7 -3x y + 2z = -4 x + 4y + 2z = 6 Solution: Write augmented matrix with coefficient matrix augmented with constant column  EMBED Equation.BREE4  Enter this 3 x 4 matrix into calculator and call it A. On main screen, go to MATRIX, then MATH, then choose rref( Input the matrix you are going to be taking the rref of, namely, rref([A]) and hit enter. Out pops the reduced row echelon form (RREF) of the matrix, where you can read the answers. This problem results in a RREF of  EMBED Equation.BREE4  and we can reinterpret into math equations, that is, 1x + 0y + 0z = 0 or x = 0 0x + 1y + 0z = 2 or y = 2 0x + 0y + 1z = -1 or z = -1 and our solution is (0, 2, -1) which we could check in. RREF stands for Reduced Row Echelon Form which means you could get a matrix that looks like where the left 3 columns is I, the identity matrix, and the last .column is your solution. RREF can also be used for inconsistent systems and consistent dependent systems, unlike using Cramers Rule or using inverse matrices to solve the equation where you just get error messages. If result looks like  EMBED Equation.BREE4  and we can recognize that we have Identity on left, we have solutions on right  Consistent Independent (5, 3, 2) would be classification and solution If result looks like  EMBED Equation.BREE4  and we can recognize that we have DO NOT have Identity on left, we see that bottom row shows 0 = 2 which is false Inconsistent No solution would be classification and solution If result looks like  EMBED Equation.BREE4  and we can recognize that we DO NOT have Identity on left, we see that bottom row shows 0 = 0 which is true! Write equations from first two rows: 1x + 0y + 0z = 5 or x = 5 and y + z = 3 solve y in terms of z or z in terms of y: y = 3 z Consistent Dependent (5, 3 z, z) is one way to give family of solutions. would be classification and solutions  EMBED Equation.BREE4  01L    6 7 8 9 ; V W n o p q R z | } ǿ|oddYhxh;CJaJhxhtCJaJj>hy'hIEHUjb=R hIUVj hy'hIEHUj`=R hIUVh/jhy'hIEHUj`=R hIUVhIjhIUh/hICJaJhxhICJaJhICJaJh/CJaJhth;CJaJh LCJaJ"KL   { | pqkdX $$Ifl,"" t0644 lap ytx$If & F$IfgdI $IfgdI 庲啄ujXGu!jthxhICJEHUaJ#jgK hxhICJUVaJhxhICJaJjhxhICJUaJ!j hxh;CJEHUaJ#jYK hxh;CJUVaJhxh/CJaJh/CJaJhtCJaJ!j hxh;CJEHUaJ#jӋK hxh;CJUVaJhxh;CJaJjhxh;CJUaJ| OkdJ$$IflF ,"   t06    44 lapytx $IfgdI$If         ɸ步q`N#jK hxhICJUVaJ!jhxh CJEHUaJ#jK hxh CJUVaJjhxh CJUaJhxh/CJaJh/CJaJhtCJaJhxh;CJaJ!jhxhICJEHUaJ#jK hxhICJUVaJhxhICJaJjhxhICJUaJhxh CJaJ  ! 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