Advertisements
Advertisements
Question
Determine the values of a and b so that the following matrices are singular:
A = `[(7, 3),(-2, "a")]`
Solution
A = `[(7, 3),(-2, "a")]`
|A| = `[(7, 3),(-2, "a")]`
|A| = 7a + 6
Given that A is singular
∴ |A| = 0
7a + 6 = 0
⇒ a = `(-6)/7`
APPEARS IN
RELATED QUESTIONS
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")`
Show that `|(x + 2"a", y + 2"b", z + 2"c"),(x, y, z),("a", "b", "c")|` = 0
Write the general form of a 3 × 3 skew-symmetric matrix and prove that its determinant is 0
Prove that `|(1, "a", "a"^2 - "bc"),(1, "b", "b"^2 - "ca"),(1, "c", "c"^2 - "ab")|` = 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:
`|(x + y, y + z, z + x),(z, x, y),(1, 1, 1)|`
If A and B are square matrices of order 3 such that |A| = –1 and |B| = 3, find the value of |3AB|
Determine the roots of the equation `|(1,4, 20),(1, -2, 5),(1, 2x, 5x^2)|` = 0
Show that `|("b" + "c", "a" - "c", "a" - "b"),("b" - "c", "c" + "a", "b" - "a"),("c" - "b", "c" - "a", "a" + b")|` = 8abc
Identify the singular and non-singular matrices:
`[(1, 2, 3),(4, 5, 6),(7, 8, 9)]`
If cos 2θ = 0, determine `[(theta, costheta, sintheta),(costheta, sintheta, 0),(sintheta, 0, costheta)]^2`
Choose the correct alternative:
The value of the determinant of A = `[(0, "a", -"b"),(-"a", 0, "c"),("b", -"c", 0)]` is
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
Let a, b, c, d be in arithmetic progression with common difference λ. If `|(x + a - c, x + b, x + a),(x - 1, x + c, x + b),(x - b + d, x + d, x + c)|` = 2, then value of λ2 is equal to ______.
If `x∈R|(8, 2, x),(2, x, 8),(x, 8, 2)|` = 0, then `|x/2|` is equal to ______.
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 ______.
