5. Find A-1 and A4 if 3 0 0 0 0-1 -1 0 0 A = 0 0 1/2 0 .0 00 1

Q: (D4 + 3D3 – 6D² – 28D – 24)y = 0 (D3 + 3D2 + 3D + 2)y = 0 -

A: 2) (D3+3D2+3D+2)y=0 The auxiliary equation is…

Q: Show that for baetween ( tana

A: Show that for x between π4,1 for the function tanxx=32.

Q: Let S be a linear transformation from R³ to R² with associated matrix Let T be a linear…

A: Let  be a linear transformation from  to  with associated matrix .Let  be a linear transformation…

Q: Q2] Find the lower bound of Iz - 3|if |z - il < 1

A:

Q: 7. If F{f} = [1, 1+ i, –2i, 2i, 1– i] then compute F{f©f}.

A:

Q: Pove that 3-1 multiple of 2 for 1. is

A:

Q: Show that the entire function cosh(z) takes every value in C infinitely many times.

A: The function cosh(z) is the hyperbolic cosine of z and is defined as:cosh(z)=ez+e−z2We are…

Q: 10) tind tre area of tve region boonded by the Graphs Of tre Given functions y- 2-x* ,4= 2-4X The…

A:

Q: Let X~N(10,9). Find P(Z > -2)

A: It is given that, X~N(10,9)

Q: IF Z= Cos o+isin@ prove i tan %3D 2. 1ナて

A: we use Trigonometry identities to solve this Question

Q: Let a € R, and define vectors u₁, U2, U3 € R³ in terms of a by E] 2 U₂ = a U₁ = 3a +3 2a +3 a² + 3a]…

A:

Q: 0.2 Differentiate In x+1, with respect to x. x²-x+1

A:

Q: Prove that x² +¸µ111² +21112 where prime denotes differentiation w.r.t.s. = 1 o² + 1+p¹² P

A:

Q: with Zeros of 2i with integer coeRficients that haf E Puno

A: We need to find the polynomial of degree three with integer coefficient

Q: find the'mters ection d Exe sy,z]= [a,0,31++ 4,-2,178 [+sy,z]=[6,-12,--11]+5 [1,2,4]?

A:

Q: Prove that coth-la = In x +1 for |a| > 1 x - 1

A:

Q: Q1. Find the image of the set A= [-2 under function sin x.

A:

Q: Prove that if AERnxm then rank(A) = rank(AT)

A: If A ∈ Rnxm then we have to prove that rank(A) = rank(AT)

Q: : Does fcz) = Continuous af cis

A: We have to solve given problem:

Q: Suppose that z is a function of z and y and that ze y cos z. Find and

A:

Q: 4. If /(r.y)=- , find f, and f,. V+y

A:

Q: B) Show that coth-x = In ()

A:

Q: Prove 2- = =4 has infinite many Solu thans ZEC.

A:

Q: Sketch ler=qcose

A: The given curve is  1-r2=9cos(θ)

Q: Let φ1(x) = 1, φ2(x) = x/|x|, φ3(x) = x^2 − 1/3 for −1 ≤x ≤1. Show that (φ1,φ2,φ3) form an…

A:

Q: let foo- X-1 when x+i- Féndavalde of fethat calil makefis continueus at xe

A: For a function f(x) to be continuous at x = a the condition is:

Q: Prove that f, uv v • dỉ = – §̟ vũu • dĩ

A: Whenever the force is conservative in nature the work done over the closed loop is always zero. i.e…

Q: - Find V x+y `

A: Given that, fx,y=x+yx-y We have to find ∇f. We know that, ∇f=∇x+yx-y=∂f∂x,∂f∂y

Q: If ACX,find A' for(X.I)

A:

Q: A small high school has 30 seniors, 20 juniors, and 10 sophomores. If 3 students are chosen from…

A:

Q: Find the deriratire of y tanx usim the Difinition Rule

A: Given that:y=tanxTo find its derivative.

Q: Find ell eigen eigen elues eipeo vect ors of T(x, x2 ** )=(Xxy xXg --- ) ... ..-

A: See the attachment

Q: As PQR in sicle Circl 2²4²25 Such that & & Rone (3,4) &(-4,3) fmd <Q PR?

A: Given that PQR is a triangle, which is inside the circle  such that P and Q are (-4,3) and (3,4)…

Q: 4. Prove that the interval (0, 1) does not contain a smallest value x.

A:

Q: aF O F2 aF, If F = F,I+Fj +F,k then prove that div F = + ду

A: