Advertisements
Advertisements
प्रश्न
Find the rank of the following matrices
`((-1, 2, -2),(4, -3, 4),(-2, 4, -4))`
Advertisements
उत्तर
Let A = `((-1, 2, -2),(4, -3, 4),(-2, 4, -4))`
Order of A is 3 × 3
∴ p(A) ≤ 3
Consider the third order minor = `|(-1, 2, -2),(4, -3, 4),(-2, 4, -4)|`
= – 1(12 – 16) – 2(– 16 + 8) – 2(16 – 6)
= – 1(– 4) – 2(– 8) – 2(10)
= 4 + 16 – 20
= 0
Since the third order minor vanishes, therefore
∴ p(A) ≠ 3
Consider a second order minor = `|(-1, 2),(4, -3)|`
= 3 – 8
= – 5 ≠ 0
There is a minor of order 2, which is not zero.
∴ p(A) = 2
APPEARS IN
संबंधित प्रश्न
Solve the following system of equations by rank method
x + y + z = 9, 2x + 5y + 7z = 52, 2x – y – z = 0
Show that the following system of equations have unique solutions: x + y + z = 3, x + 2y + 3z = 4, x + 4y + 9z = 6 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:
The rank of m n × matrix whose elements are unity is
Choose the correct alternative:
The rank of the unit matrix of order n is
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:
The rank of the diagonal matrix `[(1, , , , ,),(, 2, , , ,),(, , -3, , ,),(, , , 0, ,),(, , , , 0,),(, , , , ,0)]`
Choose the correct alternative:
If |A| ≠ 0, then A is
Find the rank of the matrix
A = `((-2, 1, 3, 4),(0, 1, 1, 2),(1, 3, 4, 7))`
Find k if the equations x + y + z = 1, 3x – y – z = 4, x + 5y + 5z = k are inconsistent
