Advertisements
Advertisements
Question
Find the rank of the following matrices
`((2, -1, 1),(3, 1, -5),(1, 1, 1))`
Advertisements
Solution
Let A = `((2, -1, 1),(3, 1, -5),(1, 1, 1))`
Order of A is 3 × 3
∴ p(A) ≤ 2
Consider the third order minor = `|(2, -1, 1),(3, 1, -5),(1, 1, 1)|`
= 2(1 + 5) – (– 1) (3 + 5) + 1 (3 – 1)
= 2 (6) + 1(8) + 1(2)
= 12 + 8 + 2
= 22 ≠ 0
There is a minor of order 3, which is not zero
∴ p(A) = 3
APPEARS IN
RELATED QUESTIONS
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.
The price of three commodities, X, Y and Z are and z respectively Mr. Anand purchases 6 units of Z and sells 2 units of X and 3 units of Y. Mr.Amar purchases a unit of Y and sells 3 units of X and 2 units of Z. Mr. Amit purchases a unit of X and sells 3 units of Y and a unit of Z. In the process they earn ₹ 5,000/-, ₹ 2,000/- and ₹ 5,500/- respectively. Find the prices per unit of three commodities by rank method
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:
If p(A) = p(A,B)= then the system is
Choose the correct alternative:
If p(A) = p(A, B)= the number of unknowns, then the system is
Choose the correct alternative:
If the number of variables in a non-homogeneous system AX = B is n, then the system possesses a unique solution only when
Choose the correct alternative:
If `|"A"_("n" xx "n")|` = 3 and |adj A| = 243 then the value n is
Find k if the equations x + y + z = 1, 3x – y – z = 4, x + 5y + 5z = k are inconsistent
