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Solve system of linear equations, using matrix method 5x+2y=4,

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Solve system of linear equations, using matrix method
$5 x + 2 y = 4, 7 x + 3 y = 5$

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Solve system of linear equations, using matrix method

5 x + 2 y = 4, 7 x + 3 y = 5

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Text solutionVerified

Given system of equations

5 x + 2 y = 4

7 x + 3 y = 5

This can be written as

A X = B

where

A = [5723], X = [x y], B = [45]

Here,

∣ A ∣ = 15 - 14 = 1

Since,

∣ A ∣ \neq = 0

Hence,

A^{- 1}

exists and the system has a unique solution given by

X = A^{- 1} B

A^{- 1} = \frac{a d j A}{∣ A ∣}

and

a d j A = C^{T}

So, we will find the co-factors of each element of

A

C_{11} = (- 1)^{1 + 1} 3 = 3

C_{12} = (- 1)^{1 + 2} 7 = - 7

C_{21} = (- 1)^{2 + 1} 2 = - 2

C_{22} = (- 1)^{2 + 2} 5 = 5

So, the co-factor matrix is

[3 - 2 - 7 5]

\Rightarrow a d j A = C^{T} = [3 - 7 - 2 5]

\Rightarrow A^{- 1} = \frac{a d j A}{∣ A ∣} = [3 - 7 - 2 5]

The solution is

X = A^{- 1} B

[x y] = [3 - 7 - 2 5] [45]

= [12 - 10 - 28 + 25]

\Rightarrow [x y] = [2 - 3]

Hence,

x = 2, y = - 3

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Question Text	Solve system of linear equations, using matrix method $5 x + 2 y = 4, 7 x + 3 y = 5$
Answer Type	Text solution:1
Upvotes	150