Let A be a nxn square matrix having rank 2 then rank of (A^t A) is (A^t- Transpose of A) Option A)) exactly 2 Option B)) exactly 1 Option C)) may be 2, not exactly

Q: In a medical trial on COVID 19, there were 230 patients, 78 people received treatment A 81 people…

A: In the Venn diagram, the set notation is shown as

Q: 4. Which of the following subsets of R³ constitute a subspace of R³? [Here, x = (₁, §2, §3).] (a)…

A:

Q: (3) The solution of the following problem for the wave equation on the entire real-line: that=Uz…

A:

Q: Let f be a function which has an inverse and let f(-1) = 2. If Q is the surface of revolution…

A: As per the question we are given an invertible function f such that f(-1) = 2 And Q is the surface…

Q: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

A: This is a problem of multi-variable calculus.

Q: 8). Prove the validity of the arguments using the method of conditional proof. a). p → q (qvr) → s…

A:

Q: 3. Let zo be an isolated singularity of f. Then Res(f'(2), 20) =

A: As per the company rule, we are supposed to solve one problem from a set of multiple problems.…

Q: function √x² + y² + 1 x² + y² 2 f(x, y) = 1 if (x, y) = (0,0) 2 2 (x, y) = (0,0). If not, classify…

A:

Q: 5. z = yex+x Iny xey-y lnx

A: Solution : z=yex+xln(y)xey-yln(x) zx=∂z∂x =∂ ∂ xyex+xlnyxey-ylnx-∂ ∂ xxey-ylnxyex+xlnyxey-ylnx2…

Q: 4. Evaluate ryz dV, S is the solid in the first octant S bounded by the cylinders x² + y² = 4 and x²…

A:

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral…

A: Let  I= ∫π4π2ln(tanx)dx Here, a=π4 , b=π2 , f(x) =ln(tanx) Step size h=b-1n=π2-π410=π410=π40 Then…

Q: Let f C D be a function, with C being the domain and D being the codomain. Show that for any C₁, C₂…

A: Solution: Let  x ∈ fc1∩c2⇒∃  y∈ c1∩c2such that fy=x⇒y∈ c1 and y∈ c2⇒fy ∈ fc1 and fy ∈ fc2⇒fy ∈ fc1∩…

Q: a 1 - x²) cos(nx) dx F(x 一九 4 sin(nл) — 4nл соs(nл) — 2n²л² sin(n) πη3

A:

Q: Solve the system of differential equations. Jx₁' = 6x12x2 x2 = 2x1 + 10x2 x₁(0) = 16, x₂(0) = − 16…

A:

Q: 4. Consider the matrix equation Ax = b where, A = a b 1 1 where a, b > 0. (a) When is A strictly…

A:

Q: Thando furniture manufacturer, determines that in order to sell x chairs, the price per chair in…

A:

Q: m above, prove that for every real number c>0, there is a 1/N < c.

A: In every real number c, there is integer N which is N &gt; c.

Q: Q5: Consider the following subsets of real plane R² Determine with graph: 1-Arewise connected A=…

A: Follow the steps.

Q: Find the Laurent expansion of g(z) = (2-1)/[2³3 +32² + 2z] in i) 0 < 2 <1 ii) 3<|2| iii) 0<z +2 <1

A:

Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = 9y-y² and y = 2x

A: Given: Let us consider the given parabola is given as, x=9y-y2 and y=2x. Let's determine the moment…

Q: A. SOLUTION OF NON-HOMOGENEOUS SYSTEM GIVEN: 7 -3 4 0 -71 A-2 1-1 4 6 010-3 -5 3. SOLVE THE SYSTEM…

A: A=7-340-721-146010-3-5 WE HAVE TO FIND LU FACTORIZATION.

Q: Prove that (Z(sqrt(2)),+,×) is an integral domain

A:

Q: . Show that the vectors V1=(0, 3, 1, -1); V2=(6, 0, 5, 1); V3=(4, -7, 1, 3) form a linearly…

A:

Q: Problem 25. Find the Laurent expansion of f(z) = 1/[2(2-1)(z-2)] in i) 0 < 2 <1 ii) 1<|z| <2 2 < |z|…

A: This question from laurent series of complex analysis.

Q: (a) Solve the first order linear ordinary differential equation dy x sin x- + (sin x + x cos x) y =…

A: We have given a first order linear differential equation ,  x sin(x) dydx + sin(x) + x cos(x)y = xex…

Q: Find vectors A and B such that A is parallel to (2, 1,-1), B is perpendicular to (2, 1, -1) and A +…

A:

Q: The general solution for the linear homogeneous system depends only on the free variables and there…

A:

Q: QUESTION 3 A manager wishes to simulate 10 days of operation of an inventory system. The beginning…

A: Solution :-

Q: The logistic growth equation is represented by the equation: dN Nrmox (1-7) dt =

A: Introduction: There are many different types of population models. All the models are based upon the…

Q: Q2 Using forward and backward difference approximations of O(h) and centered difference d²y…

A:

Q: Consider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line  I with…

A:

Q: (k) The solution of the following problem for the heat equation with nonhomge- neous boundary…

A:

Q: Evaluate the following integral e(-t²-25) dt

A: The integral given is as follows: ∫0∞e-t2-254t2dt We know that a complementary error function is…

Q: Is (fe5x dx) = e5x ? dx True O False Reset Selection

A: ddx∫e5xdx=e5x

Q: - 23 + 132-та -3 наха +2+12 (; +ана - -7³ 2 э

A: We have to write the given expression -λ3+13λ-12 as a product of linear factors. For this, we have…

Q: 8. If Z is an (n−1)-dimensional subspace of an n-dimensional vector space X, show that Z is the null…

A: Given: n-1 dimensional subspace To find: Scalar multiple

Q: 5. The von Bertalanffy equation is defined by the ODE W'(t) = aw (t)-BW (t) where is a constant…

A: The von Bertalanffy equation is defined by ODE as follows W'(T) = αW(t)2-βW(t)Let  y(t) = W1-λdWdt =…

Q: 0 < x < 1 1< <2 2 <지

A:

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral…

A: Here the lower limit is π4 and upper limit is π2

Q: Consider the polar curves C₁:r = 3 (blue) and C₂: r = 2 − 2sin0 (red) and let R be the shaded region…

A:

Q: 5. ) Write an equation for the graph of the rational function shown. Explain your reasoning. 5. 4 -8…

A: Given the graph is

Q: The gradient of the tangent to the curve (image attached)   at  x = 2  is  4. The value of  a  is…

A: The gradient or the slope of the tangent to the curve: y=fx at x=a is f'a.  It is known that…

Q: y- y' cos x = y² cos x (1 - sin x)

A:

Q: (f. g)'(2) =

A: Real valued function: A function whose domain and codomain are subsets of the set of real numbers ℝ…

Q: Solve this problem. Show your complete answer with a graph in a given-required-solution format…

A: Here follow the graph of the region bounded.

Q: b) ABC company intends to select company representatives for the beach volleyball event tournament…

A: Given that , there are 21 games in which  both the players are women and 45 games in which  both the…

Q: Finding the Determinants using Elementary Row Operations E = 2 1 3 1 10 11 0210 0 1 23 1 1 -2 -7 0 1…

A:

Q: 14. If d is a metric on a vector space X‡ {0} which is obtained from a norm, and å is defined by…

A:

Q: c. The quadric S can also be identified as a surface of revolution. Find a generating curve for S on…

A: Given,  S: 4x2-(y-3)2+4z2=4 is a surface of revolution Since the coefficient of x2 and z2 are same,…

Q: 34) True or False: The transformation shown below is a rotation.

A: Introduction: Symmetricity is very important in geometry. When a line divides a geometrical pattern…