anonymous
  • anonymous
What is the value for the coefficient determinant (D) in the following system? 4x – 3y = 16 3x + 7y = –25
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
im trying to finish a thirteen assignments on flvs as fast as possible i know how to do them im just trying to get some shortcuts asap sorry but ill rate you as best response though for the consideration...
anonymous
  • anonymous
I suppose you are trying to apply Linear Algebra. Indeed you can express a system as a linear transformation and consider the determinant of the matrix representation. If the determinant is non-zero there is a unique solution and if it is zero there could either be multiple solutions or no solutions at all.
anonymous
  • anonymous
This is true because a non-zero determinant implies full rank which implies a one to one and onto linear transformation which implies a unique solution.

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anonymous
  • anonymous
you check calculator my eye not see good
anonymous
  • anonymous
What he is looking for is a matrix representation of the system. I will show you how to set it up and compute the determinant.
anonymous
  • anonymous
I don't have good eye may be Alchemista show you
anonymous
  • anonymous
7* (4x – 3y = 16 ) 28x-21y=112 3* (3x + 7y = –25 9x+21y=-75 ------------ 37x+ 0y = 37 x= 37/37 x =1 substitution x = 1 find y can you find y?
anonymous
  • anonymous
substitution x = 1 find y 4x – 3y = 16 3x + 7y = –25
anonymous
  • anonymous
dannycobb5215 are you able find y?
anonymous
  • anonymous
go back original equation substitution x=1 than solve for y 4x – 3y = 16 3x + 7y = –25 use first or second equation
anonymous
  • anonymous
First we rewrite the system. $$\left(\begin{array}{cc} 4 & -3 \\ 3 & 7 \end{array}\right) \left(\begin{array}{c} x \\ y \end{array}\right) = \left(\begin{array}{c} 16 \\ -25 \end{array}\right)$$ Computing the determinant of a \(2 \times 2\) matrix is rather easy. $$\textbf{det }\left(\begin{array}{cc} a & b \\ c & d \end{array}\right) = ad - bc$$ Now we compute the determinant of the system above. \((4 \cdot 7) - (-3 \cdot 3) = 37\) A non-zero determinant, therefore the system has a unique solution.
anonymous
  • anonymous
?
anonymous
  • anonymous
You didn't read his question: "What is the value for the coefficient determinant (D) in the following system?" He didn't ask for a solution to the system, he asked for the so called "coefficient determinant".

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