Advertisements
Advertisements
Question
Choose the correct alternative:
if Δ = `|("a", "b", "c"),(x, y, z),("p", "q", "r")|` then `|("ka", "kb","kc"),("k"x, "k"y, "k"z),("kp", "kq", "kr")|` is
Options
Δ
kΔ
3kΔ
k3Δ
Advertisements
Solution
k3Δ
APPEARS IN
RELATED QUESTIONS
Prove that `|(1 + "a", 1, 1),(1, 1 + "b", 1),(1, 1, 1 + "c")| = "abc"(1 + 1/"a" + 1/"b" + 1/"c")`
Prove that `|(1, "a", "a"^2 - "bc"),(1, "b", "b"^2 - "ca"),(1, "c", "c"^2 - "ab")|` = 0
Show that `|("a"^2 + x^2, "ab", "ac"),("ab", "b"^2 + x^2, "bc"),("ac", "bc", "c"^2 + x^2)|` is divisiible by x4
If A and B are square matrices of order 3 such that |A| = –1 and |B| = 3, find the value of |3AB|
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:
A = `[(7, 3),(-2, "a")]`
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)]`
Find the value of the product: `|(log_3 64, log_4 3),(log_3 8, log_4 9)| xx |(log_2 3, log_8 3),(log_3 4, log_3 4)|`
Choose the correct alternative:
If ⌊.⌋ denotes the greatest integer less than or equal to the real number under consideration and – 1 ≤ x < 0, 0 ≤ y < 1, 1 ≤ z ≤ 2, then the value of the determinant `[([x] + 1, [y], [z]),([x], [y] + 1, [z]),([x], [y], [z] + 1)]`
If Δ is the area and 2s the sum of three sides of a triangle, then
If P1, P2, P3 are respectively the perpendiculars from the vertices of a triangle to the opposite sides, then `cosA/P_1 + cosB/P_2 + cosC/P_3` is equal to
If f(x) = `|(cos^2x, cosx.sinx, -sinx),(cosx sinx, sin^2x, cosx),(sinx, -cosx, 0)|`, then for all x
Find the area of the triangle with vertices at the point given is (1, 0), (6, 0), (4, 3).
`|("b" + "c", "c", "b"),("c", "c" + "a", "a"),("b", "a", "a" + "b")|` = ______.
If `|(1 + x, x, x^2),(x, 1 + x, x^2),(x^2, x, 1 + x)|` = ax5 + bx4 + cx3 + dx2 + λx + µ be an identity in x, where a, b, c, d, λ, µ are independent of x. Then the value of λ is ______.
