IGNOU BEY 18 SOLVED ASSIGNMENT

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BEY 18: Linear Algebra and Calculus

Title Name	IGNOU BEY 18 SOLVED ASSIGNMENT
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	BACHELOR DEGREE PROGRAMMES
Course Code	BSCAEY
Course Name	Bachelor of Science (Applied Science-Energy)
Subject Code	BEY 18
Subject Name	Linear Algebra and Calculus
Year	2025
Session	-
Language	English Medium
Assignment Code	BEY 18/Assignment-1/2025
Product Description	Assignment of BSCAEY (Bachelor of Science (Applied Science-Energy)) 2025. Latest BEY 018 2026 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU BEGC-131 (BAG) 2025-26 Assignment is for January 2026 Session: 30th September, 2026 (for December 2025 Term End Exam). Semester Wise January 2025 Session: 30th March, 2026 (for June 2026 Term End Exam). July 2025 Session: 30th September, 2025 (for December 2025 Term End Exam).
Format	Ready-to-Print PDF (.soft copy)

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BEY 18 2025 - English

Assignment -4

(To be done after studying the course material)

Course Code: BEY-018

Course Title: Linear Algebra and Calculus

Assignment Code: BEY-018/TMA/2025

Maximum Marks: 100

Last Date of Submission: May 31, 2025 (For June TEE), September 30, 2025 (For December TEE)

Note:

1. All questions are compulsory. Marks for the questions are shown within the brackets on the right side.

Q.1 a) If A, B are symmetric matrices of the same order, then what will be the type of matrix (AB-BA)? Give reasons in support of your answer.

b) If the matrix A is both symmetric and skew-symmetric, then determine A.

c) If A is a square matrix, such that A² =A, then find (I + A)³ - 7A.

d) $ext{If}A=egin{bmatrix}1&0&0\0&1&1\0&-2&4end{bmatrix},quad I=egin{bmatrix}1&0&0\0&1&0\0&0&1end{bmatrix},quad A^{-1}=frac{1}{6}(A^2+aA+bI) ext{Find}:a ext{:and:}b.$

Q.2 a) $vec{a}=hat{i}+hat{j}+hat{k}$ , and $vec{b}=hat{j}-hat{k}$ find vector $vec{c}$ such that $vec{a}:x:vec{c}:=:vec{b}$ and $vec{a}.vec{c}=3$

Show that area of a parallelogram whose diagonals are given by $vec{a}$ and $vec{b}$ is $frac{|vec{a} imesvec{b}|}{2}$ Also find the area of the parallelogram whose diagonals are $2hat{i}-hat{j}+hat{k}$ and $hat{i}-3hat{j}+2hat{k}$

Q.3 a) Find a vector of magnitude 6, which is perpendicular to both the vectors $2hat{j}-hat{j}+2hat{k}$ and $4hat{i}-hat{j}+3hat{k}$

b) Find the angle between the vectors $2hat{i}-hat{j}+hat{k}$ and $3hat{i}+4hat{j}-hat{k}$ .

c) If $vec{a}+vec{b}+vec{c}=0$ , show that $vec{a}$ x $vec{b}$ = $vec{b}$ x $vec{c}$ = $vec{c}$ x $vec{a}$ .

d) If A,B,C,D are the points with position vectors $hat{i}+hat{j}-hat{k},quad 2hat{i}-hat{j}+3hat{k},quad 3hat{i}-2hat{j}+hat{k}$ , respectively. Find the projection of $overrightarrow{AB}$ along $overrightarrow{CD}$ .

e) Using vectors, find the area of the triangle ABC with vertices A(1,2,3), B(2, -1, 4) and C(4,5,-1).

Q.4 a) Prove that

$egin{vmatrix}b+c&a&a\c&c+a&a\b&a&a+bend{vmatrix}=4abc$

b) Prove that

$egin{vmatrix}1&bc&bc(b+c)\1&ca&ca(c+a)\1&ab&ab(a+b)end{vmatrix}$ is independent of a, b, c.

Q.5 a) Show that the conical tent of given capacity will require the least amount of canvas if its height is √2 times its base radius.

b) An open storage bin with square base and vertical sides is to be constructed from a given amount of material. Determine its dimensions if its volume is to be maximum neglecting the thickness of material and waste in constructing it.

c) Find the height of a right cylinder with greatest lateral surface area that may be inscribed in a given sphere of radius R.

d) Given a point on the axis of the parabola y² = 2px at a distance a from the vertex, find the abscissa of the point of the curve closest to it.

e)Can Rolle's theorem be applied to each of the following functions? Find 'c' in case it can be applied.

i. f(x) = sin² x on the interval [0, π].

ii. f (x) = x² + 4 on [-2, 2].

iii. f(x) = sinx + cos x on $left[0,frac{pi}{2} ight]$

iv. f(x) = x³- 2x on [0, 1].

Q.6 a) Explain why Lagrange's mean value theorem is not applicable to the following functions in the respective intervals: f(x) = 13x +11, x∈ [1,3].

b) Verify means values theorem for the function f(x) = 4x³-4x in the interval [a,b], where a=0, and b=3.

c) Find 'c' of Cauchy's mean value theorem for the function f(x) = 2.ln(x) and g(x) = x²-1 in the interval [2,3].

Q.7 Find the first order partial derivatives

a) $z=frac{p^2(r+1)}{t^3}+pr e^{2p+3r+4t}$

b) $g(s,t,v)=t^2ln(s+2t)-ln(3v)(s^3+t^2-4v)$

c) Find $frac{partial z}{partial x}$ and $frac{partial z}{partial y}$ for the function x² sin(y³)+xe^3z-cos(z²)=3y-6z+8

Q.8 a) Find the orthogonal trajectories of the family of circles x² + (y - c)² = c², where c is a parameter.

b) In a certain isolated population p (t) the rate of population growth $frac{dp}{dt}$ is equal to $p-frac{k}{varepsilon}p^2$ , where k and ɛ are both positive constants. If p (0) = 1, then find the limiting population as t→ ∞.

Q.9 a) Use the method of Laplace transforms to find the solution of the initial value problem y" + 9y = 6 cos 3t, y(0) = 2, y'(0) = 0

b) Determine the solution of the undamped (forced vibrations) system mü + Ku = F_o cos wt, u(0) = 0, u(0) = 1 When, w ≠ $sqrt{frac{k}{m}}$

Q.10 a) Reduce the equation

xy" + y' + xy = 0, x > 0

into Bessel's equation and hence write its general solution in terms of Bessel's functions.

b) Prove that

$4J_n''+2J_n(x)=J_{n-2}(x)+J_{n+2}(x)$

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