Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Solve the system of equations, using matrix method 5x+2y=3, 3

Question

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

Views: 1,023 students

Found 8 tutors discussing this question

Emma Discussed

Solve the system of equations, using matrix method

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

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

Given system of equations

5 x + 2 y = 3

3 x + 2 y = 5

This can be written as

A X = B

where

A = [5322], X = [x y], B = [35]

Here,

∣ A ∣ = 10 - 6 = 4

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} 2 = 2

C_{12} = (- 1)^{1 + 2} 3 = - 3

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

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

So, the co-factor matrix is

[2 - 2 - 3 5]

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

\Rightarrow A^{- 1} = \frac{a d j A}{∣ A ∣} = \frac{1}{4} [2 - 3 - 2 5]

The solution is

X = A^{- 1} B

[x y] = \frac{1}{4} [2 - 3 - 2 5] [35]

[x y] = \frac{1}{4} [6 - 10 - 9 + 25]

\Rightarrow [x y] = [- 1 4]

Hence,

x = - 1, y = 4

Was this solution helpful?

150

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes

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