Advertisements
Advertisements
Question
Without expanding, evaluate the following determinants:
`|(x + y, y + z, z + x),(z, x, y),(1, 1, 1)|`
Advertisements
Solution
`|(x + y, y + z, z + x),(z, x, y),(1, 1, 1)| =|(x + y + z, x + y + z, x + y + z),(z, x, y),(1, 1, 1)|`
`"R"_1 = "R"_1 +"R"_2`
= `(x + y + z)|(1, 1, 1),(z, x, y),(1, 1, 1)|` = 0
∵ R1 = R3
APPEARS IN
RELATED QUESTIONS
Show that `|("b" + "c", "bc", "b"^2"C"^2),("c" + "a", "ca", "c"^2"a"^2),("a" + "b", "ab", "a"^2"b"^2)|` = 0
Write the general form of a 3 × 3 skew-symmetric matrix and prove that its determinant is 0
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|
Solve that `|(x + "a", "b", "c"),("a", x + "b", "c"),("a", "b", x + "c")|` = 0
Find the area of the triangle whose vertices are (0, 0), (1, 2) and (4, 3)
Identify the singular and non-singular matrices:
`[(2, -3, 5),(6, 0, 4),(1, 5, -7)]`
Identify the singular and non-singular matrices:
`[(0, "a" - "b", "k"),("b" - "a", 0, 5),(-"k", -5, 0)]`
If cos 2θ = 0, determine `[(theta, costheta, sintheta),(costheta, sintheta, 0),(sintheta, 0, costheta)]^2`
Choose the correct alternative:
If A = `[(1, -1),(2, -1)]`, B = `[("a", 1),("b", -1)]` and (A + B)2 = A2 + B2, then the values of a and b are
Choose the correct alternative:
The value of x, for which the matrix A = `[("e"^(x - 2), "e"^(7 + x)),("e"^(2 + x), "e"^(2x + 3))]` is singular
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
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
Find the area of the triangle with vertices at the point given is (1, 0), (6, 0), (4, 3).
Choose the correct option:
Let `|(0, sin theta, 1),(-sintheta, 1, sin theta),(1, -sin theta, 1 - a)|` where 0 ≤ θ ≤ 2n, then
Let S = `{((a_11, a_12),(a_21, a_22)): a_(ij) ∈ {0, 1, 2}, a_11 = a_22}`
Then the number of non-singular matrices in the set S is ______.
If a, b, c, are non zero complex numbers satisfying a2 + b2 + c2 = 0 and `|(b^2 + c^2, ab, ac),(ab, c^2 + a^2, bc),(ac, bc, a^2 + b^2)|` = ka2b2c2, then k is equal to ______.
