Advertisements
Advertisements
प्रश्न
The maximum value of `|(1, 1, 1),(1, (1 + sintheta), 1),(1, 1, 1 + costheta)|` is `1/2`
पर्याय
True
False
उत्तर
This statement is True.
Explanation:
Let Δ = `|(1, 1, 1),(1, (1 + sintheta), 1),(1, 1, 1 + costheta)|`
C1 → C1 – C2, C2 → C2 – C3
= `|(0, 0, 1),(-sintheta, sintheta, 1),(0, -costheta, 1 + costheta)|`
Expanding along C3
= `1|(-sintheta, sintheta),(0, -costheta)|`
= sin θ cos θ – 0
= sin θ cos θ
= `1/2 * 2 sin theta cos theta`
= `1/2 sin 2theta`
= `1/2 xx 1` ......[Maximum value of sin 2θ = 1]
= `1/2`
APPEARS IN
संबंधित प्रश्न
If A = `[(1,1,-2),(2,1,-3),(5,4,-9)]`, Find |A|
Find values of x, if ` |(2,4),(5,1)|=|(2x, 4), (6,x)|`
Using the property of determinants and without expanding, prove that:
`|(x, a, x+a),(y,b,y+b),(z,c, z+ c)| = 0`
Use properties of determinants to solve for x:
`|(x+a, b, c),(c, x+b, a),(a,b,x+c)| = 0` and `x != 0`
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.
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?
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
Show that Δ = `|(x, "p", "q"),("p", x, "q"),("q", "q", x)| = (x - "p")(x^2 + "p"x - 2"q"^2)`
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)|` = ______.
The determinant ∆ = `|(cos(x + y), -sin(x + y), cos2y),(sinx, cosx, siny),(-cosx, sinx, cosy)|` is independent of x only.
If A = `[(2, lambda, -3),(0, 2, 5),(1, 1, 3)]`, then A–1 exists if ______.
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 A and B are matrices of order 3 and |A| = 5, |B| = 3, then |3AB| = 27 × 5 × 3 = 405.
`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 A = `[(1,0,0),(2,"cos x","sin x"),(3,"sin x", "-cos x")],` then det. A is equal to ____________.
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" =` ____________.
In a third order matrix aij denotes the element of the ith row and the jth column.
A = `a_(ij) = {(0",", for, i = j),(1",", f or, i > j),(-1",", f or, i < j):}`
Assertion: Matrix ‘A’ is not invertible.
Reason: Determinant A = 0
Which of the following is correct?
