Advertisements
Advertisements
प्रश्न
Without expanding, evaluate the following determinants:
`|(2, 3, 4),(5, 6, 8),(6x, 9x, 12x)|`
Advertisements
उत्तर
`|(2, 3, 4),(5, 6, 8),(6x, 9x, 12x)| = x|(2, 3, 4),(5, 6, 8),(6, 9, 12)|`
= `(x)(3)|(2, 3, 4),(5, 6, 8),(2, 3, 4)|`
= 3x (0)
= 0
∴ R1 = R2
APPEARS IN
संबंधित प्रश्न
Show that `|("b" + "c", "bc", "b"^2"C"^2),("c" + "a", "ca", "c"^2"a"^2),("a" + "b", "ab", "a"^2"b"^2)|` = 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)|`
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, b, c, are all positive, and are pth, qth and rth terms of a G.P., show that `|(log"a", "p", 1),(log"b", "q", 1),(log"c", "r", 1)|` = 0
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
If A = `[(1/2, alpha),(0, 1/2)]`, prove that `sum_("k" = 1)^"n" det("A"^"k") = 1/3(1 - 1/4)`
If A and B are square matrices of order 3 such that |A| = –1 and |B| = 3, find the value of |3AB|
Verify that det(AB) = (det A)(det B) for A = `[(4, 3, -2),(1, 0, 7),(2, 3, -5)]` and B = `[(1, 3, 3),(-2, 4, 0),(9, 7, 5)]`
Show that `|(1, 1, 1),(x, y, z),(x^2, y^2, z^2)|` = (x – y)(y – z)(z – x)
If (k, 2), (2, 4) and (3, 2) are vertices of the triangle of area 4 square units then determine the value of k
Identify the singular and non-singular matrices:
`[(0, "a" - "b", "k"),("b" - "a", 0, 5),(-"k", -5, 0)]`
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 `|(2"a", x_1, y_1),(2"b", x_2, y_2),(2"c", x_3, y_3)| = "abc"/2 ≠ 0`, then the area of the triangle whose vertices are `(x_1/"a", y_1/"a"), (x_2/"b", y_2/"b"), (x_3/"c", y_3/"c")` is
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
Choose the correct alternative:
If x1, x2, x3 as well as y1, y2, y3 are in geometric progression with the same common ratio, then the points (x1, y1), (x2, y2), (x3, y3) are
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
A pole stands vertically inside a triangular park ΔABC. If the angle of elevation of the top of the pole from each corner of the park is same, then in ΔABC the foot of the pole is at the
`|("b" + "c", "c", "b"),("c", "c" + "a", "a"),("b", "a", "a" + "b")|` = ______.
