Advertisements
Advertisements
प्रश्न
If x = – 4 is a root of Δ = `|(x, 2, 3),(1, x, 1),(3, 2, x)|` = 0, then find the other two roots.
उत्तर
Applying R1 → (R1 + R2 + R3), we get
`|(x + 4, x + 4, x + 4),(1, x, 1),(3, 2, x)|`
Taking (x + 4) common from R1, we get
Δ = `(x + 4) |(1, 1, 1),(1, x, 1),(3, 2, x)|`
Applying C2 → C2 – C1, C3 → C3 – C1 , we get
Δ = `(x + 4)|(1, 0, 0),(1, x - 1, 0),(3, -1, x - 3)|`
Expanding along R1,
∆ = (x + 4)[(x – 1)(x – 3) – 0].
Thus, ∆ = 0 implies x = – 4, 1, 3.
APPEARS IN
संबंधित प्रश्न
If A = `[(1,1,-2),(2,1,-3),(5,4,-9)]`, Find |A|
A matrix A of order 3 × 3 has determinant 5. What is the value of |3A|?
On expanding by first row, the value of the determinant of 3 × 3 square matrix
\[A = \left[ a_{ij} \right]\text{ is }a_{11} C_{11} + a_{12} C_{12} + a_{13} C_{13}\] , where [Cij] is the cofactor of aij in A. Write the expression for its value on expanding by second column.
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.
A matrix of order 3 × 3 has determinant 2. What is the value of |A (3I)|, where I is the identity matrix of order 3 × 3.
Which of the following is not correct?
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
Without expanding, show that Δ = `|("cosec"^2theta, cot^2theta, 1),(cot^2theta, "cosec"^2theta, -1),(42, 40, 2)|` = 0
The determinant ∆ = `|(cos(x + y), -sin(x + y), cos2y),(sinx, cosx, siny),(-cosx, sinx, cosy)|` is independent of x only.
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 x + y + z = 0, prove that `|(x"a", y"b", z"c"),(y"c", z"a", x"b"),(z"b", x"c", y"a")| = xyz|("a", "b", "c"),("c", "a", "b"),("b", "c", "a")|`
Let f(t) = `|(cos"t","t", 1),(2sin"t", "t", 2"t"),(sin"t", "t", "t")|`, then `lim_("t" - 0) ("f"("t"))/"t"^2` is equal to ______.
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 a matrix of order 3 × 3, then |3A| = ______.
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)|` = ______.
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 = ______.
If A = `[(1,0,0),(2,"cos x","sin x"),(3,"sin x", "-cos x")],` then det. A is equal to ____________.
Find the minor of the element of the second row and third column in the following determinant `[(2,-3,5),(6,0,4),(1,5,-7)]`
If `Delta = abs((5,3,8),(2,0,1),(1,2,3)),` then write the minor of the element a23.
If `"abc" ne 0 "and" abs ((1 + "a", 1, 1),(1, 1 + "b", 1),(1,1,1 + "c")) = 0, "then" 1/"a" + 1/"b" + 1/"c" =` ____________.
Find the 5th term of expansion of `(x^2 + 1/x)^10`?
For positive numbers x, y, z, the numerical value of the determinant `|(1, log_x y, log_x z),(log_y x, 1, log_y z),(log_z x, log_z y, 1)|` is
