Home
Class 12
MATHS
Solve system of linear equations, using ...

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

Text Solution

Verified by Experts

5x+2y=3
3x+2y = 5
`rArr" "[{:(5,2),(3,2):}][{:(x),(y):}]=[{:(3),(5):}]rArrAX=B`
`therefore" "A=[{:(5,2),(3,2):}]`
`rArr" "|A|=[{:(5,2),(3,2):}]=10-6=4ne0`
`therefore` A is invertible
`"Now "A_(11)=2,A_()12)=-3, A_(21=-2, A_(22)=5`
`therefore" adk A"=[{:(2,-3),(-2,5):}]=[{:(2,-2),(-3,5):}]`
`"and "A^(-1)=1/|A|"adjA=1/4[{:(2,-3),(-3,5):}]`
From equation (1)
`AX=B rArr X+A^(-1)B`
`=[{:(x),(y):}]=1/4[{:(2,-2),(-3,5):}][{:(3),(5):}]=1/4[{:(6-10),(-9+25):}]=[{:(-1),(4):}]`
`therefore `x=-1, y-4
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN|Exercise Exercise 4.5|18 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|23 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|18 Videos

Similar Questions

Explore conceptually related problems

Solve system of linear equations,using matrix method,2.x3x+4y=3

Solve system of linear equations,using matrix method,x-y2x+yx+y+z=2

Solve system of linear equations,using matrix method,quad 5x+2y=47x+3y=5

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

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

Solve system of linear equations, using matrix method, in {:(x-y+2z=7),(3x+4y-5z=-5),(2x-y+3z=12):}

Solve the following system of linear equations using matrix inversion method: 5x-3y = -13, 2x+ 5y = 1.

Solve system of linear equations,using matrix method,quad 2x+3y+3z=5x-2y+z=-43x-y-2z=3

Solve system of linear equations, using matrix method, in questions 7 to 14. x-y+2z=7, 3x+4y-5z=-5, 2x-y+3z=12

Solve system of linear equations,using matrix method,2x+y+z=1x-2y-z=(3)/(2)3y-5z=9