Advertisements
Advertisements
प्रश्न
Using cofactors of elements of second row, evaluate |A|, where A = `[(5, 3, 8),(2, 0, 1),(1, 2, 3)]`
उत्तर
A = `[(5, 3, 8),(2, 0, 1),(1, 2, 3)]`
Cofactr of 2, A21 = `(- 1)^(2 + 1) |(3, 8),(2, 3)|`
= – [9 – 16]
= 7
Cofactr of 0, A22 = `(- 1)^(2 + 2) |(5, 8),(1, 3)|`
= 15 – 8
= 7
Cofactr of 1, A23 = `(- 1)^(2 + 3) |(5, 3),(1, 2)|`
= – [10 – 3]
= – 7
∴ |A| = a21 A21 + a22 A22 + a23 A23
= 2 × 7 + 0 × 7 + 1 × – 7
= 14 – 7
|A| = 7
APPEARS IN
संबंधित प्रश्न
Without expanding the determinant, prove that `|("s", "a"^2, "b"^2 + "c"^2),("s", "b"^2, "c"^2 + "a"^2),("s", "c"^2, "a"^2 + "b"^2)|` = 0
Prove that `|("a"^2, "bc", "ac" + "c"^2),("a"^2 + "ab", "b"^2, "ac"),("ab", "b"^2 + "bc", "c"^2)| = 4"a"^2"b"^2"c"^2`
Prove that `|(1 + "a", 1, 1),(1, 1 + "b", 1),(1, 1, 1 + "c")| = "abc"(1 + 1/"a" + 1/"b" + 1/"c")`
Write the general form of a 3 × 3 skew-symmetric matrix and prove that its determinant is 0
If a, b, c are pth, qth and rth terms of an A.P, find the value of `|("a", "b", "c"),("p", "q", "r"),(1, 1, 1)|`
Find the value of `|(1, log_x y, log_x z),(log_y x, 1, log_y z),(log_z x, log_z y, 1)|` if x, y, z ≠ 1
Without expanding, evaluate the following determinants:
`|(2, 3, 4),(5, 6, 8),(6x, 9x, 12x)|`
If A and B are square matrices of order 3 such that |A| = –1 and |B| = 3, find the value of |3AB|
Solve the following problems by using Factor Theorem:
Show that `|(x, "a", "a"),("a", x, "a"),("a", "a", x)|` = (x – a)2 (x + 2a)
Show that `|("b" + "c", "a" - "c", "a" - "b"),("b" - "c", "c" + "a", "b" - "a"),("c" - "b", "c" - "a", "a" + b")|` = 8abc
Show that `|("b" + "C", "a", "a"^2),("c" + "a", "b", "b"^2),("a" + "b", "c", "c"^2)|` = (a + b + c)(a – b)(b – c)(c – a)
Show that `|(1, 1, 1),(x, y, z),(x^2, y^2, z^2)|` = (x – y)(y – z)(z – x)
Find the area of the triangle whose vertices are (0, 0), (1, 2) and (4, 3)
Determine the values of a and b so that the following matrices are singular:
B = `[("b" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]`
If cos 2θ = 0, determine `[(theta, costheta, sintheta),(costheta, sintheta, 0),(sintheta, 0, costheta)]^2`
Choose the correct alternative:
If A = `[("a", x),(y, "a")]` and if xy = 1, then det(AAT) is equal to
Choose the correct alternative:
If A = `|(-1, 2, 4),(3, 1, 0),(-2, 4, 2)|` and B = `|(-2, 4, 2),(6, 2, 0),(-2, 4, 8)|`, then B is given by
If Δ is the area and 2s the sum of three sides of a triangle, then
Choose the correct option:
Let `|(0, sin theta, 1),(-sintheta, 1, sin theta),(1, -sin theta, 1 - a)|` where 0 ≤ θ ≤ 2n, then
`|("b" + "c", "c", "b"),("c", "c" + "a", "a"),("b", "a", "a" + "b")|` = ______.
