Advertisements
Advertisements
प्रश्न
If f(x) = `|((1 + x)^17, (1 + x)^19, (1 + x)^23),((1 + x)^23, (1 + x)^29, (1 + x)^34),((1 +x)^41, (1 +x)^43, (1 + x)^47)|` = A + Bx + Cx2 + ..., then A = ______.
Advertisements
उत्तर
If f(x) = `|((1 + x)^17, (1 + x)^19, (1 + x)^23),((1 + x)^23, (1 + x)^29, (1 + x)^34),((1 +x)^41, (1 +x)^43, (1 + x)^47)|` = A + Bx + Cx2 + ..., then A = 0.
Explanation:
Given that `|((1 + x)^17, (1 + x)^19, (1 + x)^23),((1 + x)^23, (1 + x)^29, (1 + x)^34),((1 +x)^41, (1 +x)^43, (1 + x)^47)|` = A + Bx + Cx2 + ...
Taking (1 + x)17, (1 + x)23 and (1 + x)41 common from R1, R2 and R3 respectively
`(1 + x)^17 * (1 + x)^23 * (1 + x)^41 |(1, (1 + x)^2, (1 x)^6),(1, (1 + x)^6, (1 + x)^11),(1, (1 + x)^2, (1 + x)^6)|`
`(1 + x)^17 * (1 + x)^23 * (1 + x)^41 * 0` ....(R1 and R3 are identical)
∴ 0 = A + Bx + Cx2 + …
By comparing the like terms, we get A = 0.
APPEARS IN
संबंधित प्रश्न
If A = `[(1,1,-2),(2,1,-3),(5,4,-9)]`, find |A|.
Find the value of x, if `|(2,4),(5,1)|=|(2x, 4), (6,x)|`.
Find the value of x, if `|(2,3),(4,5)|=|(x,3),(2x,5)|`.
Using the property of determinants and without expanding, prove that:
`|(x, a, x+a),(y,b,y+b),(z,c, z+ c)| = 0`
Without expanding at any stage, find the value of:
`|(a,b,c),(a+2x,b+2y,c+2z),(x,y,z)|`
A matrix A of order 3 × 3 has determinant 5. What is the value of |3A|?
Let A = [aij] be a square matrix of order 3 × 3 and Cij denote cofactor of aij in A. If |A| = 5, write the value of a31 C31 + a32 C32 a33 C33.
If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A–1) = (det A)k.
Which of the following is not correct?
Which of the following is not correct in a given determinant of A, where A = [aij]3×3.
If A is a matrix of order 3 and |A| = 8, then |adj A| = __________ .
Solve the following system of linear equations using matrix method:
3x + y + z = 1
2x + 2z = 0
5x + y + 2z = 2
Show that Δ = `|(x, "p", "q"),("p", x, "q"),("q", "q", x)| = (x - "p")(x^2 + "p"x - 2"q"^2)`
If x, y ∈ R, then the determinant ∆ = `|(cosx, -sinx, 1),(sinx, cosx, 1),(cos(x + y), -sin(x + y), 0)|` lies in the interval.
The determinant ∆ = `|(sqrt(23) + sqrt(3), sqrt(5), sqrt(5)),(sqrt(15) + sqrt(46), 5, sqrt(10)),(3 + sqrt(115), sqrt(15), 5)|` is equal to ______.
If a1, a2, a3, ..., ar are in G.P., then prove that the determinant `|("a"_("r" + 1), "a"_("r" + 5), "a"_("r" + 9)),("a"_("r" + 7), "a"_("r" + 11), "a"_("r" + 15)),("a"_("r" + 11), "a"_("r" + 17), "a"_("r" + 21))|` is independent of r.
If a + b + c ≠ 0 and `|("a", "b","c"),("b", "c", "a"),("c", "a", "b")|` 0, then prove that a = b = c.
Prove tha `|("bc" - "a"^2, "ca" - "b"^2, "ab" - "c"^2),("ca" - "b"^2, "ab" - "c"^2, "bc" - "a"^2),("ab" - "c"^2, "bc" - "a"^2, "ca" - "b"^2)|` is divisible by a + b + c and find the quotient.
If f(x) = `|(0, x - "a", x - "b"),(x + "b", 0, x - "c"),(x + "b", x + "c", 0)|`, then ______.
If x, y, z are all different from zero and `|(1 + x, 1, 1),(1, 1 + y, 1),(1, 1, 1 + z)|` = 0, then value of x–1 + y–1 + z–1 is ______.
There are two values of a which makes determinant, ∆ = `|(1, -2, 5),(2, "a", -1),(0, 4, 2"a")|` = 86, then sum of these number is ______.
If A is invertible matrix of order 3 × 3, then |A–1| ______.
If A is a matrix of order 3 × 3, then (A2)–1 = ______.
`|(0, xyz, x - z),(y - x, 0, y z),(z - x, z - y, 0)|` = ______.
The maximum value of `|(1, 1, 1),(1, (1 + sintheta), 1),(1, 1, 1 + costheta)|` is `1/2`
The value of the determinant `abs ((1,0,0),(2, "cos x", "sin x"),(3, "sin x", "cos x"))` is ____________.
If `Delta = abs((5,3,8),(2,0,1),(1,2,3)),` then write the minor of the element a23.
Let A be a square matrix of order 2 x 2, then `abs("KA")` is equal to ____________.
Find the 5th term of expansion of `(x^2 + 1/x)^10`?
The value of determinant `|(sin^2 13°, sin^2 77°, tan135°),(sin^2 77°, tan135°, sin^2 13°),(tan135°, sin^2 13°, sin^2 77°)|` is
