Determine with the properties whether the function is a linear transformation, if not justify your answer with counter argument. T: M22 - R,T(B) = |B| Write standard basis and the dimension for the vector spaces of polynomial of degree seven or less i.e., Pz. Show that B = : 3 has no real eigenvalues.

Q: nd the values of the scalars a, b, c such that -2,1, –3) = a(2, -1,1) + b(1,3,–2) + c(-2,1,–3) %3D

A:

Q: If B is the standard basis of the space P, of polynomials, then let B= (1,tt.t). Use coordinate…

A: Given that B=1,t,t2,t3 be the standard basis of the space ℙ3 of polynomials. and a set of…

Q: Let A = -127 0 -8 4 0 and 6- = 36 7 Define the linear transformation T: R2 → R³ by T(x) = Ar. Find a…

A:

Q: Define a linear operator (transformation) on R2 by performing the following operations in order: (i)…

A:

Q: Explain why S is not a basis for R². S = {(-6,4)} OS is linearly dependent. OS does not span R². O S…

A: Given: S=-6, 4. We have to explain why S is not a basis for R2.

Q: show that the given vector functions are linearly dependent on (−∞,∞).

A:

Q: Find an orthonormal basis of the plane ¤1 + 5x2 – x3 = 0. %3D

A:

Q: (d) Show that the polynomials P₁ = 3 + 2x + x², P₂ = 2x+3x², p3= −2+x=2x² form a basis of the vector…

A: Using 1+2x-x^2=ap1+bp2+cp3 find a b c

Q: Show that S = {t+1,t-1,(t-1)2} be a basis of P2, the vector space of all second-degree real…

A:

Q: Find a basis of the linear space V of all 3 x 3 matrices A for which both | - A 1 and are…

A: We have to find the basis of linear space V.

Q: Let T : R2 → P2 be a linear transformation, and let B= {u1 = [1 2] , u2 = [2 5] }be a basis for R2.…

A:

Q: M2r2 is the vector space consisting of all 2x2 real matrices. The linear transformation T: M2r2 x →…

A:

Q: If B is the standard basis of the space P3 of polynomials, then let B = {1, t, t², 13³). Use…

A:

Q: Let {u₁, U₂, U3, U4} be the orthogonal basis for R¹ given below. Write x as a sum of two vectors v₁…

A:

Q: Determine whether B={1-31²,2+t-5t².1+2t) is a basis for P2.

A:

Q: Explain why S is not a basis for P2. S = {1 - x, 1 - x², -1 - 4x + 5x2} O sis linearly dependent. O…

A:

Q: Problem 10. Consider the following set of polynomials in P₁: S = {1+ 3t² +t³, 1+t+ 2t³ + 3t¹, t+t² +…

A: We know that two vectors are linearly dependent if one vector can be written as a scalar multiple of…

Q: Let T₁: R³ R4 be a linear transformation where (in the standard basis) 1 4 7 326 4 69 1 1 1/ A = Let…

A:

Q: 1,3x-2 4. Determine whether the veltors X-I and X²-3x+2 dve lihearly independent or dependent in Pz…

A: