Math Problem Statement

Write a vector equation that is equivalent to the system of equations 2 x subscript 1 space plus thin space 4 x subscript 2 space plus thin space 2 x subscript 3 space minus space 6 x subscript 4 space equals space 2 x subscript 1 plus space 2 x subscript 2 space plus space 3 x subscript 3 space minus space 9 x subscript 4 space equals space 5 A. 2 x with rightwards harpoon with barb upwards on top space plus thin space 4 y with rightwards harpoon with barb upwards on top space plus thin space 2 z with rightwards harpoon with barb upwards on top space minus space 6 w with rightwards harpoon with barb upwards on top space equals space 2 B. open square brackets table row cell 2 x subscript 1 end cell row cell x subscript 1 end cell end table close square brackets space plus space open square brackets table row cell 4 x subscript 2 end cell row cell 2 x subscript 2 end cell end table close square brackets space plus thin space open square brackets table row cell 2 x subscript 3 end cell row cell 3 x subscript 3 end cell end table close square brackets space plus space open square brackets table row cell negative 6 x subscript 4 end cell row cell negative 9 x subscript 4 end cell end table close square brackets space equals 2 C. open square brackets table row 2 4 2 cell negative 6 end cell 2 row 1 2 3 cell negative 9 end cell 5 end table close square brackets D. open square brackets table row 2 4 2 cell negative 6 end cell row 1 2 3 cell negative 9 end cell end table close square brackets open square brackets table row cell x subscript 1 end cell row cell x subscript 2 end cell row cell x subscript 3 end cell row cell x subscript 4 end cell end table close square brackets space equals open square brackets table row 2 row 5 end table close square brackets E. x subscript 1 open square brackets table row 2 row 1 end table close square brackets space plus space x subscript 2 open square brackets table row 4 row 2 end table close square brackets space plus thin space x subscript 3 open square brackets table row 2 row 3 end table close square brackets space plus space x subscript 4 open square brackets table row cell negative 6 end cell row cell negative 9 end cell end table close square brackets space equals open square brackets table row 2 row 5 end table close square brackets F. 2 open square brackets table row cell x subscript 1 end cell row cell x subscript 2 end cell end table close square brackets space plus space 4 open square brackets table row cell x subscript 1 end cell row cell x subscript 2 end cell end table close square brackets space plus thin space 2 open square brackets table row cell x subscript 1 end cell row cell x subscript 2 end cell end table close square brackets space minus space 6 open square brackets table row cell x subscript 1 end cell row cell x subscript 2 end cell end table close square brackets space equals space open square brackets table row 2 row 5 end table close square brackets

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Vector Equations
Matrices
Systems of Linear Equations

Formulas

Vector equation form: A * x = b
Matrix multiplication for systems of equations

Theorems

Matrix-vector multiplication
Representation of systems of linear equations in matrix form

Suitable Grade Level

Grades 10-12