Math Problem Statement

Perform one step of row reduction, in order to calculate the values for x and y by back substitution. Then calculate the values for x and y. Also calculate the determinant of the original matrix. ( Note: since the determinant is unchanged by type 3 row operations, it will be easier to calculate the determinant of the row reduced matrix.)

\left[\begin{array}{cc} 7 &27\cr 9 &-11 \end{array}\right] \left\lbrack \begin{array}{c} x \ y \end{array} \right\rbrack

\left[\begin{array}{c} 5\cr 2 \end{array}\right]

\left.\vphantom{\begin{array}{c}!\strut\!\strut\!\strut\\end{array}}\right[ 7 27 \left.\vphantom{\begin{array}{c}!\strut\!\strut\!\strut\\end{array}}\right] 0 \left.\vphantom{\begin{array}{c}!\strut\!\strut\!\strut\\end{array}}\right[ x \left.\vphantom{\begin{array}{c}!\strut\!\strut\!\strut\\end{array}}\right] y

\left.\vphantom{\begin{array}{c}!\strut\!\strut\!\strut\\end{array}}\right[ 5 \left.\vphantom{\begin{array}{c}!\strut\!\strut\!\strut\\end{array}}\right]

x =

y =

\mbox{det} =

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Row Reduction
Gaussian Elimination
Determinants
Back Substitution

Formulas

Row Reduction: R2 -> R2 - (9/7)R1
Back Substitution
Determinant: det(A) = ad - bc

Theorems

Gaussian Elimination
Properties of Determinants

Suitable Grade Level

College level (Linear Algebra)