Advertisements
Advertisements
Question
The determinant ∆ = `|(cos(x + y), -sin(x + y), cos2y),(sinx, cosx, siny),(-cosx, sinx, cosy)|` is independent of x only.
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
Apply R1 → R1 + sinyR2 + cosyR3, and expand
APPEARS IN
RELATED QUESTIONS
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)|`
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.
A matrix A of order 3 × 3 is such that |A| = 4. Find the value of |2 A|.
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| = __________ .
Show that Δ = `|(x, "p", "q"),("p", x, "q"),("q", "q", x)| = (x - "p")(x^2 + "p"x - 2"q"^2)`
If Δ = `|(0, "b" - "a", "c" - "a"),("a" - "b", 0, "c" - "b"),("a" - "c", "b" - "c", 0)|`, then show that ∆ is equal to zero.
If x = – 4 is a root of Δ = `|(x, 2, 3),(1, x, 1),(3, 2, x)|` = 0, then find the other two roots.
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 ______.
The value of the determinant ∆ = `|(sin^2 23^circ, sin^2 67^circ, cos180^circ),(-sin^2 67^circ, -sin^2 23^circ, cos^2 180^circ),(cos180^circ, sin^2 23^circ, sin^2 67^circ)|` = ______.
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.
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 ______.
If A = `[(2, lambda, -3),(0, 2, 5),(1, 1, 3)]`, then A–1 exists if ______.
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 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 and B are matrices of order 3 and |A| = 5, |B| = 3, then |3AB| = 27 × 5 × 3 = 405.
The maximum value of `|(1, 1, 1),(1, (1 + sintheta), 1),(1, 1, 1 + costheta)|` is `1/2`
`abs ((1 + "a", "b", "c"),("a", 1 + "b", "c"),("a", "b", 1 + "c")) =` ____________
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.
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" =` ____________.
Let A be a square matrix of order 2 x 2, then `abs("KA")` is equal to ____________.
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
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
