Advertisements
Advertisements
Question
Choose the correct alternative:
If A = `[(3/5, 4/5),(x, 3/5)]` and AT = A–1, then the value of x is
Options
`(-4)/5`
`(-3)/5`
`3/5`
`4/5`
Advertisements
Solution
`(-4)/5`
APPEARS IN
RELATED QUESTIONS
Solve the following system of linear equations by matrix inversion method:
2x + 5y = – 2, x + 2y = – 3
Solve the following system of linear equations by matrix inversion method:
2x + 3y – z = 9, x + y + z = 9, 3x – y – z = – 1
If A = `[(-5, 1, 3),(7, 1, -5),(1, -1, 1)]` and B = `[(1, 1, 2),(3, 2, 1),(2, 1, 3)]`, Find the products AB and BA and hence solve the system of equations x + y + 2z = 1, 3x + 2y + z = 7, 2x + y + 3z = 2
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:
`3/2 + 2y = 12, 2/x + 3y` = 13
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
A fish tank can be filled in 10 minutes using both pumps A and B simultaneously. However, pump B can pump water in or out at the same rate. If pump B is inadvertently run in reverse, then the tank will be filled in 30 minutes. How long would it take each pump to fill the tank by itself? (Use Cramer’s rule to solve the problem)
Solve the following systems of linear equations by Gaussian elimination method:
2x – 2y + 3z = 2, x + 2y – z = 3, 3x – y + 2z = 1
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.)
Choose the correct alternative:
If A = `[(1, tan theta/2),(- tan theta/2, 1)]` and AB = I2, then B =
Choose the correct alternative:
If A = `[(2, 3),(5, -2)]` be such that λA–1 = A, then λ 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
