Advertisements
Advertisements
Question
Solve the following system of linear equation using matrix method:
`1/x + 1/y +1/z = 9`
`2/x + 5/y+7/z = 52`
`2/x+1/y-1/z=0`
Advertisements
Solution
`Let 1/x=X; 1/y=Y;1/Z= Z`
X+Y+Z = 9 ....(1)
`2X+5Y+7Z=52` ....(2)
`2X+Y-Z =0 ` .....(3)
AX = B
`[(1, 1, 1),(2,5,7),(2,1,-1)][(X),(Y),(Z)]=[(9),(52),(0)]`
`R_2 rArr R_2- R_1 and R_3 rArr R_3 - 2R_1`
`[(1, 1, 1),(0,3,5),(0,-1,-3)][(X),(Y),(Z)]=[(9),(34),(-18)]`
`R_2rArr R_2+.3R_3`
`[(1, 1, 1),(0,0,-4),(0,-1,-3)][(X),(Y),(Z)]=[(9),(-20),(-18)]`
`[(X+Y+Z),(-4Z),(-Y -3Z)]_(3xx1) =[(9),(-20),(-18)]_(3xx1)`
∴ -4Z =-20 ⇒ Z=5
∴ -Y- 3Z = -18
∴ Y + 3Z= -18
∴Y + 15 = 18
∴ Y = 3
∴ X+Y+Z =9
∴ X + 3+ 5+9
X=1
∴ `1/X = x rArr 1/1= x` ∴ x=1
`1/Y = 3` ∴ `1/3 = y`
`1/Z = z` ∴ `z=1/5`
APPEARS IN
RELATED QUESTIONS
State, whether the following statement is true or false. If false, give a reason.
If A and B are two matrices of orders 3 × 2 and 2 × 3 respectively; then their sum A + B is possible.
Solve for a, b and c; if `[(-4, a + 5),(3, 2)] = [(b + 4, 2),(3, c- 1)]`
Find x and y from the given equations:
`[(-8, x)] + [(y, -2)] = [(-3, 2)]`
Evaluate:
`2[(-1 0)/(2 -3)] +[(3 3)/(5 0)]`
State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.
A – B = B – A
State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.
(A + B) . C = A . C + B . C
State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.
(A – B)2 = A2 – 2A . B + B2
If M = `[(2,1),(1,-2)] `; find M2, M3 and M5.
Find the inverse of the matrix A=`[[1,2],[1,3]]` using elementry transformations.
Classify the following matrix :
`|(800),(521)|`
`[(2, -1),(5, 1)]`
`[(3),(0),(-1)]`
`[(0, 0, 0),(0, 0, 0)]`
If a matrix has 8 elements, what are the possible order it can have?
Given `[(2, 1),(-3, 4)], "X" = [(7),(6)]` the order of the matrix X
The construction of demand line or supply line is the result of using
I2 is the matrix ____________.
If A is a matrix of order m × 3, B is a matrix of order 3 × 2 and R is a matrix of order 5 × n such that AB = R, the value of m and n are ______.
Which statement defines a matrix?
In a matrix, vertical lines are called:
