Advertisements
Advertisements
Question
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
Options
2
4
3
1
Solution
1
APPEARS IN
RELATED QUESTIONS
Solve the following system of linear equations by matrix inversion method:
2x + 3y – z = 9, x + y + z = 9, 3x – y – z = – 1
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
The prices of three commodities A, B and C are ₹ x, y and z per units respectively. A person P purchases 4 units of B and sells two units of A and 5 units of C. Person Q purchases 2 units of C and sells 3 units of A and one unit of B . Person R purchases one unit of A and sells 3 unit of B and one unit of C. In the process, P, Q and R earn ₹ 15,000, ₹ 1,000 and ₹ 4,000 respectively. Find the prices per unit of A, B and C. (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:
`3/2 + 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 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).
Solve the following systems of linear equations by Gaussian elimination method:
2x – 2y + 3z = 2, x + 2y – z = 3, 3x – y + 2z = 1
An amount of ₹ 65,000 is invested in three bonds at the rates of 6%, 8% and 9% per annum respectively. The total annual income is ₹ 4,800. The income from the third bond is ₹ 600 more than that from the second bond. Determine the price of each bond. (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 `("AB")^-1 = [(12, -17),(-19, 27)]` and `"A"^-1 = [(1, -1),(-2, 3)]` then `"B"^-1` =
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