Advertisements
Advertisements
प्रश्न
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
उत्तर
`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
संबंधित प्रश्न
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.
State, whether the following statement is true or false. If false, give a reason.
Transpose of a square matrix is a square matrix.
Find x and y from the given equations:
`[(5, 2),(-1, y - 1)] - [(1, x - 1),(2, -3)] = [(4, 7),(-3, 2)]`
Given : M = `[(5, -3),(-2, 4)]`, find its transpose matrix Mt. If possible, find M + Mt
State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.
A . (B – C) = A . B – A . C
Classify the following matrix :
`|(800),(521)|`
Classify the following matrix :
`|(1 , 1),(0,9)|`
Find the values of a and b) if [2a + 3b a - b] = [19 2].
If B = `|(15 , 13),(11,12),(10,17)|` , find the transpose of matrix Band If possible find the sum of the two matrices. If not possible state the reason.
If A = `|("p","q"),(8,5)|` , B = `|(3"p",5"q"),(2"q" , 7)|` and if A + B = `|(12,6),(2"r" , 3"s")|` , find the values of p,q,r and s.
Let A = `|(3 , 2),(0 ,5)|` and B = `|(1 ,0),(1 ,2)|` , find (i) (A + B)(A - B) (ii) A2 - B2 . Is (i) equal to (ii) ?
Solve the equation x + y = 4 and 2x - y = 5 using the method of reduction.
Solve the equations x + y = 4 and 2x - y = 5 using the method of reduction.
Solve the following minimal assignment problem :
| Machines | Jobs | ||
| I | II | III | |
| M1 | 1 | 4 | 5 |
| M2 | 4 | 2 | 7 |
| M3 | 7 | 8 | 3 |
`[(2, -1),(5, 1)]`
Construct a 2 x 2 matrix whose elements aij are given by aij = 2i – j
Let `"M" xx [(1, 1),(0, 2)]` = [1 2] where M is a matrix.
- State the order of matrix M
- Find the matrix M
Construct a matrix A = [aij]3 × 2 whose element aij is given by
aij = `(("i" - "j")^2)/(5 - "i")`
Construct a matrix A = [aij]3 × 2 whose element aij is given by
aij = `(("i" + "j")^3)/5`
A, B and C are three matrices each of order 5; the order of matrix CA + B2 is ______.
