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If A = `([cos alpha, sin alpha],[-sinalpha, cos alpha])` , find α satisfying 0 < α < `pi/r`when `A+A^T=sqrt2I_2` where AT is transpose of A.
Concept: undefined >> undefined
Show that the differential equation `2xydy/dx=x^2+3y^2` is homogeneous and solve it.
Concept: undefined >> undefined
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Find the particular solution of the differential equation:
2y ex/y dx + (y - 2x ex/y) dy = 0 given that x = 0 when y = 1.
Concept: undefined >> undefined
If `A=[[1,2,2],[2,1,2],[2,2,1]]` ,then show that `A^2-4A-5I=0` and hence find A-1.
Concept: undefined >> undefined
Find the absolute maximum and absolute minimum values of the function f given by f(x)=sin2x-cosx,x ∈ (0,π)
Concept: undefined >> undefined
If `A=([2,0,1],[2,1,3],[1,-1,0])` find A2 - 5A + 4I and hence find a matrix X such that A2 - 5A + 4I + X = 0
Concept: undefined >> undefined
Find the local maxima and local minima, of the function f(x) = sin x − cos x, 0 < x < 2π.
Concept: undefined >> undefined
Two tailors, A and B, earn Rs 300 and Rs 400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP
Concept: undefined >> undefined
Let `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`
Find A + B
Concept: undefined >> undefined
Compute the following:
`[(a,b),(-b, a)] + [(a,b),(b,a)]`
Concept: undefined >> undefined
Compute the following:
`[(a^2+b^2, b^2+c^2),(a^2+c^2, a^2+b^2)] + [(2ab , 2bc),(-2ac, -2ab)]`
Concept: undefined >> undefined
Compute the following:
`[(-1,4, -6),(8,5,16),(2,8,5)] + [(12,7,6),(8,0,5),(3,2,4)]`
Concept: undefined >> undefined
Compute the following:
`[(cos^2x, sin^2 x),(sin^2 x ,cos^2 x)]+[(sin^2 x, cos^2 x), (cos^2 x, sin^2 x)]`
Concept: undefined >> undefined
If F(x) = `[(cosx, -sinx,0), (sinx, cosx, 0),(0,0,1)]` show that F(x)F(y) = F(x + y)
Concept: undefined >> undefined
Let A be a nonsingular square matrix of order 3 × 3. Then |adj A| is equal to ______.
Concept: undefined >> undefined
Examine the consistency of the system of equations.
x + 2y = 2
2x + 3y = 3
Concept: undefined >> undefined
Examine the consistency of the system of equations.
2x − y = 5
x + y = 4
Concept: undefined >> undefined
Examine the consistency of the system of equations.
x + 3y = 5
2x + 6y = 8
Concept: undefined >> undefined
Examine the consistency of the system of equations.
x + y + z = 1
2x + 3y + 2z = 2
ax + ay + 2az = 4
Concept: undefined >> undefined
Examine the consistency of the system of equations.
3x − y − 2z = 2
2y − z = −1
3x − 5y = 3
Concept: undefined >> undefined
