5. [§ 3.1,3.3] — Consider the plane, P , described by the equation(s) ? (a) (10...

5. [§ 3.1,3.3] — Consider the plane, P , described by the equation(s) ?

(a) (10 pts) Write the system of equations in matrix-vector form (A⃗x = ⃗b).

(b) (10 pts) Find all solutions to the system of equations. x1+x3+x4 = 0 x1+x2+3x3+5x4 = 0

(c) (10 pts) Identify a basis for P .

(d) Next, consider the orthogonal projection onto P, defined by T(⃗x) = M⃗x, M ∈ R4×4. { We do not have the tools to derive the matrix M yet. }

i. (10 pts) What is the image of T [im(T ) = im(M )]?

ii. (10 pts) What is the dimension of the image of T [dim(im(T ))]?

iii. (10 pts) What is the dimension of the kernel of T [dim(ker(T ))]?

iv. (10 pts) Identify a basis for ker(T )?

Expert Solution

Colby Messinger answered 2 years ago

A market is described by the equation Qd=100-P and Qs=P. A tax of $10 is placed...

A market is described by the equation Qd=100-P and Qs=P. A tax of $10 is placed on the seller of the product such that he will receive less to take home than the original equilibrium price. Therefore, the new supply equation becomes Qs=(p-t). Does the seller pay the whole $10 of the tax burden? How much does the seller pay? How much does the buyer pay? Why do they split the burden this way?

(a) Find the equation of the plane passing through the point P(0, 0, 5) and the...

(a) Find the equation of the plane passing through the point P(0, 0, 5) and the line x = 1 + t, y = 1 − t, z = 4 − 5t. (b) Find parametric equations for the line passing through point (1, 2, 3) and parallel to the line x = 2 − 3t, y = 4 + t, z = 2t.

Define our “universe” S as the region in the xy-plane that is described by S =...

Define our “universe” S as the region in the xy-plane that is described by S = {(x, y) : |x| + |y| ≤ 2 and y > −1} . (a) Mathematically and graphically describe three sets A1, A2, and A3 taken from S that are mutually exclusive but not collectively exhaustive. (b) Mathematically and graphically describe three sets B1, B2, and B3 taken from S that are collectively exhaustive but not mutually exclusive. (c) Mathematically and graphically describe three sets...

a. consider the plane with equation -x+y-z=2, and let p be the point (3,2,1)in R^3. find...

a. consider the plane with equation -x+y-z=2, and let p be the point (3,2,1)in R^3. find the distance from P to the plane. b. let P be the plane with normal vector n (1,-3,2) which passes through the point(1,1,1). find the point in the plane which is closest to (2,2,3)

a) Find an equation of the plane tangent to the graph of f at the given point P.

a) Find an equation of the plane tangent to the graph of f at the given point P. Write your answer in the form ax + by +cz= d, where a, b, c, and d are integers with no common factor, and a is greater or equal to 0. f(x,y)= 2x3y + 4x-y, P(1,3,7) b) Use a multivariable chain rule to find a formula for the given derivative or partial derivative. w= f(x,y), x=g(u,v), y=h(u,v); ∂w/ ∂v

For p, q ∈ S^1, the unit circle in the plane, let d_a(p, q) = min{|angle(p)...

For p, q ∈ S^1, the unit circle in the plane, let d_a(p, q) = min{|angle(p) − angle(q)| , 2π − |angle(p) − angle(q)|} where angle(z) ∈ [0, 2π) refers to the angle that z makes with the positive x-axis. Use your geometric talent to prove that d_a is a metric on S^1.

D: P=10 S: P= 1 + 2Q Tax=5 a.) Solve for the original market clearing price...

D: P=10 S: P= 1 + 2Q Tax=5 a.) Solve for the original market clearing price and quantity b.) Calculate the price elasticity of demand at the intital price c.) Calculate the price elasticity of supply at the intial price d.) On the basis of these two elasticity coefficents, anticipate the distribtuion of the burden of the tax

Consider the context-free grammar G = ( {S}, {a, b}, S, P) where P = {...

Consider the context-free grammar G = ( {S}, {a, b}, S, P) where P = { S -> aaSb | aab }. Construct a NPDA M that such that L(M) = L(G). I would like the transition graph for this NPDA please.

Digitization of signals Consider the analog signal s(t) = 5sin(500t +p 5)+ cos(200t +p 4) to...

Digitization of signals Consider the analog signal s(t) = 5sin(500t +p 5)+ cos(200t +p 4) to be transferred over a digital communications system. (a) Compute the maximum allowable sampling period that the analog-to-digital converter (ADC) must use to ensure the perfect reconstruction of the signal at the receiver. (b) What theorem governs the choice made in part (a)? (c) How many samples of the analog signal do we need to store in order to reproduce 10p seconds of it (i.e.,...

consider the curve described by the equation: 4x2 - 3xy + y2 = 14 at any...

consider the curve described by the equation: 4x2 - 3xy + y2 = 14 at any given point on this curve, we have dy/dx = -8x + 3y / -3x + 2y your task is to find the points on the curve where the tangent line is parallel to the line y = x What is the x-coordinae of the leftmost point on the curve where the tangent line is parallel to the line y= x

Question