Equivalence Theorems Linear Algebra (Invertibility)

Let A be an n*n square matrix.Prove :If Ax = b has exactly one solution for every n*1 matrix b, det(A) # 0Can you kindly explain how we can prove that, without using the definition of det(A) :... more

Can I get some help please

In this problem, distance is in meters and time is in seconds. A rocket flies vertically upwards. At time t=1 the rocket is 95m above the ground and is moving upwards with speed 70ms^−1. The... more

V is a vector space and W,U,S are subspace of V

how do i prove that (W∩U)+(W∩S)⊆W∩(U+S)?


Related Rates (Derivatives)

How to show that if the volume of a balloon is decreasing at a rate proportional to its surface area, the radius of the balloon is shrinking at a constant rate.


Find an equation of a plane containing the three points

Find an equation of a plane containing the three points(-2,-5,0), (0,0,3), (0,1,5)in which the coefficient of x is 7____________ = 0


calculate gradient and laplacian

Consider the scalar field Φ(x,y,z) = sin(-z) * e^-y + 7a) Calculate the gradient of Φ b) Calculate the Laplacian of Φ c) Is this field harmonic ? No/Yes

factor the polynomial f(x) = x^4 - 4x^3 + 16x - 16 given that 2 and -2 are zeros factored form: f(x)=

secondly identify all real zeros x=

group theory question

the link for image of the multiplication table:https://ibb.co/59RTBjmthe questionsa) Find the order of (G,°) b) Find an element x such that a°x°c = f.

Finding a Series

Find a series that diverges where each term 0 is less than or equal to an is less than 1 over n and an does not equal a over bn+c for any constants a,b, and c


Consider the volume of the space bounded by the curved surface of a cylinder

Consider the volume of the space bounded by the curved surface of a cylinder defined by x2+y2=4, z=2x2+y2, and the x-y plane. Find the volume of the cylinder using integrations in cylindrical... more


Math Linear Algebra Question

Can someone help with this question please. Prove that |iw−3| = |iw+3| if and only if w is real.

Find f'(x) of a function given f'(2x^3)?

When given the derivative of a function with a random value (eg value of d/dx f(2x3) is given), how do I calculate f'(x)? For example (switching out numbers here), given that d/dx(f(2x3)) = 5x5,... more


Elementary Matrices

When you are finding all of the elementary matrices that must be multiplied by a matrix M such that E1E2E3M=M*(RREF) Does it matter if the path you took to get Matrix M to RREF matter?what I'm... more


When x = π/3 , what is the rate of change of the area of triangle ABC?

A particle moves along the curve y = sin x starting at the origin. Its x-coordinate increases atthe rate of m units per second. The triangle has a point on the origin, and one following y = sin x


Find the polynomial function f with real coefficients that has the given degree, zeros, and solution point.

Degree 4Zeros-1,2,√2iSolution Point f(1)=24


Find the centroid of the region bounded by the curves y = 1 and y = x^2.

I haven't been able to get this one started as well. Thanks for any help you can give me


Calculus Differentiation Critical Point Question

How many critical points does the function f(x) = (x-1)x1521/2019 have in the interval [-1, 1]?


Differentiate using the quotient rule

Differentiate using the quotient rule d/dx[(cos x)/x].

Evaluating triple integrals

Consider2 √ (4-z2) 2 ∫ ∫ ∫ xz dxdydz0 0 √(y2+z2)the question is to evaluate the integral by firstly converting to cylindrical coordsand to sketch the integration... more

evaluate the integral using trigonometric substitution

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