Advertisements
Advertisements
प्रश्न
Solve the following systems of linear equations by Cramer’s rule:
`3/2 + 2y = 12, 2/x + 3y` = 13
Advertisements
उत्तर
Put `1/x` = a
⇒ 3a + 2y = 12
2a + 3y = 13
Writing the above equations in matrix form we get
`[(3, 2),(2, 3)][(x),(y)] = [(12, 13)]`
(i.e) AX = B
Now |A| = Δ = `|(3, 2),(2, 3)|` = 9 – 4 = 5 ≠ 0
Δa = `|(12, 2),(13, 3)|` = 36 – 26 = 10
Δy = `|(3, 12),(2, 13)|` = 39 – 24 = 15
a = `Delta_"a"/Delta = 10/5` = 2
y = `Delta_y/Delta = 15/5` = – 3
∴ a = 2, y = 3 but `1/x` = a
⇒ x = `1/"a" = 1/2` and y = 3
∴ x = `1/2`, y = 3
APPEARS IN
संबंधित प्रश्न
Solve the following system of linear equations by matrix inversion method:
x + y + z – 2 = 0, 6x – 4y + 5z – 31 = 0, 5x + 2y + 2z = 13
A man is appointed in a job with a monthly salary of certain amount and a fixed amount of annual increment. If his salary was ₹ 19,800 per month at the end of the first month after 3 years of service and ₹ 23,400 per month at the end of the first month after 9 years of service, find his starting salary and his annual increment. (Use matrix inversion method to solve the problem.)
Solve the following systems of linear equations by Cramer’s rule:
5x – 2y + 16 = 0, x + 3y – 7 = 0
Solve the following systems of linear equations by Cramer’s rule:
`3/x - 4/y - 2/z - 1` = 0, `1/x + 2/y + 1/z - 2` = 0, `2/x - 5/y - 4/z + 1` = 0
In a competitive examination, one mark is awarded for every correct answer while `1/4` mark is deducted for every wrong answer. A student answered 100 questions and got 80 marks. How many questions did he answer correctly? (Use Cramer’s rule to solve the problem).
A chemist has one solution which is 50% acid and another solution which is 25% acid. How much each should be mixed to make 10 litres of a 40% acid solution? (Use Cramer’s rule to solve the problem).
A family of 3 people went out for dinner in a restaurant. The cost of two dosai, three idlies and two vadais is ₹ 150. The cost of the two dosai, two idlies and four vadais is ₹ 200. The cost of five dosai, four idlies and two vadais is ₹ 250. The family has ₹ 350 in hand and they ate 3 dosai and six idlies and six vadais. Will they be able to manage to pay the bill within the amount they had?
If ax² + bx + c is divided by x + 3, x – 5, and x – 1, the remainders are 21, 61 and 9 respectively. Find a, b and c. (Use Gaussian elimination method.)
A boy is walking along the path y = ax2 + bx + c through the points (– 6, 8), (– 2, – 12), and (3, 8). He wants to meet his friend at P(7, 60). Will he meet his friend? (Use Gaussian elimination method.)
Choose the correct alternative:
If A = `[(3/5, 4/5),(x, 3/5)]` and AT = A–1, then the value of x is
Choose the correct alternative:
If A = `[(costheta, sintheta),(-sintheta, costheta)]` and A(adj A) = `[("k", 0),(0, "k")]`, then k =
Choose the correct alternative:
If adj A = `[(2, 3),(4, 1)]` and adj B = `[(1, -2),(-3, 1)]` then adj (AB) is
Choose the correct alternative:
If ρ(A) ρ([A|B]), then the system AX = B of linear equations is
Choose the correct alternative:
If 0 ≤ θ ≤ π and the system of equations x + (sin θ)y – (cos θ)z = 0, (cos θ) x – y + z = 0, (sin θ) x + y + z = 0 has a non-trivial solution then θ is
Choose the correct alternative:
The augmented matrix of a system of linear equations is `[(1, 2, 7, 3),(0, 1, 4, 6),(0, 0, lambda - 7, mu + 7)]`. This system has infinitely many solutions if
Choose the correct alternative:
Let A = `[(2, -1, 1),(-1, 2, -1),(1, -1, 2)]` and 4B = `[(3, 1, -1),(1, 3, x),(-1, 1, 3)]`. If B is the inverse of A, then the value of x is
