Advertisements
Advertisements
प्रश्न
Find the rank of the following matrices
`((1, -1),(3, -6))`
Advertisements
उत्तर
Let A = `((1, -1),(3, -6))`
Order of A is 2 × 2
∴ p(A) ≤ 2
Consider the second order minor = `|(1, -1),(3, -6)|`
= – 6 – (– 3)
= – 6 + 3
= – 3
|A| ≠ 0
There is a minor of order 2, which is not zero
∴ p(A) = 2
APPEARS IN
संबंधित प्रश्न
Find the rank of the following matrices
`((2, -1, 1),(3, 1, -5),(1, 1, 1))`
Find the rank of the following matrices
`((-1, 2, -2),(4, -3, 4),(-2, 4, -4))`
Show that the equations 5x + 3y + 7z = 4, 3x + 26y + 2z = 9, 7x + 2y + 10z = 5 are consistent and solve them by rank method
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 A = `((1),(2),(3))` then the rank of AAT is
Choose the correct alternative:
If p(A) ≠ p(A, B) =, 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:
The system of equations 4x + 6y = 5, 6x + 9y = 7 has
Choose the correct alternative:
If |A| ≠ 0, then A is
Find k if the equations x + y + z = 1, 3x – y – z = 4, x + 5y + 5z = k are inconsistent
