Advertisements
Advertisements
प्रश्न
Find the rank of the following matrices
`((1, 2, -1, 3),(2, 4, 1, -2),(3, 6, 3, -7))`
Advertisements
उत्तर
Let A = `((1, 2, -1, 3),(2, 4, 1, -2),(3, 6, 3, -7))`
Let us transform the matrix A to an echelon form by using elementary transformations.
A = `((1, 2, -1, 3),(2, 4, 1, -2),(3, 6, 3, -7))`
`∼ ((1, 2, -1, 3),(0, 0, 3, -8),(0, 0, 6, -16)) {:("R"_2 -> "R"_2 - 2"R"_1),("R"_3 -> "R"_3 - 3"R"_1):}`
`∼ ((1, 2, -1, 3),(0, 0, 3, -8),(0, 0, 0, 0)) {:"R"_3 -> "R"_3 - 3"R"_1:}`
The above matrix is in echelon form.
The number of non zero rows is 2
⇒ p(A) = 2
APPEARS IN
संबंधित प्रश्न
Find the rank of the following matrices
`((5, 6),(7, 8))`
Find the rank of the following matrices
`((1, 4),(2, 8))`
An amount of ₹ 5,000/- is to be deposited in three different bonds bearing 6%, 7% and 8% per year respectively. Total annual income is ₹ 358/-. If the income from the first two investments is ₹ 70/- more than the income from the third, then find the amount of investment in each bond by the rank method
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:
For the system of equations x + 2y + 3z = 1, 2x + y + 3z = 3, 5x + 5y + 9z = 4
Choose the correct alternative:
The system of linear equations x = y + z = 2, 2x + y – z = 3, 3x + 2y + k = 4 has unique solution, if k is not equal to
Choose the correct alternative:
If `|"A"_("n" xx "n")|` = 3 and |adj A| = 243 then the value n is
Choose the correct alternative:
Rank of a null matrix is
Find the rank of the matrix
A = `((4, 5, 2, 2),(3, 2, 1, 6),(4, 4, 8, 0))`
Find k if the equations x + y + z = 1, 3x – y – z = 4, x + 5y + 5z = k are inconsistent
