Advertisements
Advertisements
Question
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
Options
a = 4, b = 1
a = 1, b = 4
a = 0, b = 4
a = 2, b = 4
Solution
a = 1, b = 4
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 `|(sec^2theta, tan^2theta, 1),(tan^2theta, sec^2theta, -1),(38, 36, 2)|` = 0
Write the general form of a 3 × 3 skew-symmetric matrix and prove that its determinant is 0
If `|("a", "b", "a"alpha + "b"),("b", "c", "b"alpha + "c"),("a"alpha + "b", "b"alpha + "c", 0)|` = 0, prove that a, b, c are in G. P or α is a root of ax2 + 2bx + c = 0
If A = `[(1/2, alpha),(0, 1/2)]`, prove that `sum_("k" = 1)^"n" det("A"^"k") = 1/3(1 - 1/4)`
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|
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)
Identify the singular and non-singular matrices:
`[(1, 2, 3),(4, 5, 6),(7, 8, 9)]`
Determine the values of a and b so that the following matrices are singular:
A = `[(7, 3),(-2, "a")]`
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:
The value of the determinant of A = `[(0, "a", -"b"),(-"a", 0, "c"),("b", -"c", 0)]` is
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)]`
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
`|("b" + "c", "c", "b"),("c", "c" + "a", "a"),("b", "a", "a" + "b")|` = ______.
If a, b, c are positive and are the pth, qth and rth terms respectively of a G.P., then the value of `|(loga, p, 1),(logb, q, 1),(logc, r, 1)|` is ______.
If `x∈R|(8, 2, x),(2, x, 8),(x, 8, 2)|` = 0, then `|x/2|` is equal to ______.