Advertisements
Advertisements
प्रश्न
Identify the singular and non-singular matrices:
`[(0, "a" - "b", "k"),("b" - "a", 0, 5),(-"k", -5, 0)]`
Advertisements
उत्तर
Let C = `[(0, "a" - "b", "k"),("b" - "a", 0, 5),(-"k", -5, 0)]`
|C| = `|(0, "a" - "b", "k"),("b" - "a", 0, 5),(-"k", -5, 0)|`
|C| = 0 – (a – b) (0 + 5k) + k(– 5(b – a) – 0)
|C| = – 5k(a – b) – 5k(b – a)
|C| = – 5k(a – b) + 5k(a – b)
|C| = 0
∴ C is a singular matrix.
APPEARS IN
संबंधित प्रश्न
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`
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)`
If A is a Square, matrix, and |A| = 2, find the value of |A AT|
Determine the roots of the equation `|(1,4, 20),(1, -2, 5),(1, 2x, 5x^2)|` = 0
Solve the following problems by using Factor Theorem:
Show that `|(x, "a", "a"),("a", x, "a"),("a", "a", x)|` = (x – a)2 (x + 2a)
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:
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 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 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
The remainder obtained when 1! + 2! + 3! + ......... + 10! is divided by 6 is,
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 `x∈R|(8, 2, x),(2, x, 8),(x, 8, 2)|` = 0, then `|x/2|` is equal to ______.
