Answer :

Let


2u +3v + 10w =4


4u – 6v + 5w = 1


6u + 9v – 20w = 2


Writing equation as AX = B


=


A = X = B =



= (2) – (-3) + (10)


= 2 (75) – 3 (-110) + 10 (72)


= 150 + 330 + 720


= 1200 0


its inverse exists and the system of equations is consistent and has a unique solution.


AX = B


X=A-1B


A-1 = adj (A)


Adj (A) = =


A =


M11 = 120 – 45 = 75


M12 = (-80 – 30) = -110


M13 = (36 + 36) = 72


M21 = (-60 – 90) = -150


M22 =(-40 – 60) = -100


M23 = (18 – 18) = 0


M31 = (15 + 60) = 75


M32 = (10 – 40) = - 30


M33 = (-12 – 12) = - 24


(Taken from above mentioned calculations)


A11 = (-1)1+1 M11 = (-1)2 . 75 = 75


A12 = 110


A13 = 72


A21 = 150


A22 = -100


A23 = 0


A31 = 75


A32 =30


A33 =-24


Adj. A =


X = A-1 B


Putting Values,





Hence, putting back the values,


X = 2, y = 3 & z = 5.


OR


Using elementary transformation,


A = IA
















Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Using matrices, sMathematics - Board Papers

If possible, usinMathematics - Exemplar

If possible, usinMathematics - Exemplar

Using matrices, sMathematics - Board Papers

Prove that <span Mathematics - Board Papers

Find the value ofMathematics - Board Papers

If A is a <span lMathematics - Board Papers