Advertisements
Advertisements
प्रश्न
Find the rank of the following matrices
`((1, 4),(2, 8))`
Advertisements
उत्तर
Let A = `((1, 4),(2, 8))`
Order of A is 2 × 2
∴ p(A) ≤ 2
Consider the second order minor = `|(1, 4),(2, 8)|`
= 8 – 8
= 0
Since the second are minor vanishes, P(A) ≠ 2
Consider a first order minor |1| ≠ 0
There is a minor of order 1, which is not zero
∴ p(A) = 1
APPEARS IN
संबंधित प्रश्न
Find the rank of the following matrices
`((-1, 2, -2),(4, -3, 4),(-2, 4, -4))`
Find the rank of the following matrices
`((3, 1, -5, -1),(1, -2, 1, -5),(1, 5, -7, 2))`
Find the rank of the following matrices
`((1, -2, 3, 4),(-2, 4, -1, -3),(-1, 2, 7, 6))`
If A = `((1, 1, -1),(2, -3, 4),(3, -2, 3))` and B = `((1, -2, 3),(-2, 4, -6),(5, 1, -1))`, then find the rank of AB and the rank of BA.
Show that the equations 5x + 3y + 7z = 4, 3x + 26y + 2z = 9, 7x + 2y + 10z = 5 are consistent and solve them by rank method
For what values of the parameter λ, will the following equations fail to have unique solution: 3x – y + λz = 1, 2x + y + z = 2, x + 2y – λz = – 1
Choose the correct alternative:
If the rank of the matrix `[(lambda, -1, 0),(0, lambda, -1),(-1, 0, lambda)]` is 2, then λ is
Choose the correct alternative:
For the system of equations x + 2y + 3z = 1, 2x + y + 3z = 3, 5x + 5y + 9z = 4
Choose the correct alternative:
If |A| ≠ 0, then A is
Find k if the equations 2x + 3y – z = 5, 3x – y + 4z = 2, x + 7y – 6z = k are consistent
