Consider the system of linear equations w + 3x + 2y + 2z = 0 w + 4x + y = 0 3w + 5x + 10 y + 14z = 0 2w + 5x + 5y + 6z = 0 with solutions of the form (w, x, y, z), where w x, y, and z are real. Which of the following statements is FALSE?

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∻Solution by Steps∻ ‖ step 1 ⋮ To solve the system of linear equations, we can use substitution or elimination methods. The asksia-ll calculator has already provided a partial solution. ‖ ‖ step 2 ⋮ From the asksia-ll calculator, we have $ y = -w - 4x $ and $ z = \frac{1}{2} (w + 5x) $. ‖ ‖ step 3 ⋮ Substitute $ y $ and $ z $ into the first equation $ w + 3x + 2y + 2z = 0 $ to find a relationship between $ w $ and $ x $. ‖ ‖ step 4 ⋮ After substitution, the equation becomes $ w + 3x - 2w - 8x + w + 5x = 0 $. Simplify this to find the relationship between $ w $ and $ x $. ‖ ‖ step 5 ⋮ Simplifying gives $ 0w + 0x = 0 $, which implies that $ w $ and $ x $ are dependent variables and can take any real value. ‖ ∻Answer∻ ⚹ The system has infinitely many solutions of the form $ (w, x, -w - 4x, \frac{1}{2} (w + 5x)) $, where $ w $ and $ x $ are any real numbers. ⚹ ∻Key Concept∻ ⚹System of Linear Equations with Infinitely Many Solutions⚹ ∻Explanation∻ ⚹In a system of linear equations, if the equations are dependent and do not contradict each other, the system has infinitely many solutions. The solution set can be expressed in terms of one or more free variables.⚹◊What is the determinant of the coefficient matrix in the system of linear equations provided by the student?⍭ Generate me a similar question◊

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