1.2 Find a basis B for the domain of I Suh that the mahix for ī alative to Bis iagend. Hogand. T: R²¬R: T(x ]) = (22 + 2y, x+j) %3D 行 B:

Q: Let L: R → R³ be defined by L (a) Find the representation of L with respect to the nat- ural basis S…

A: Given: L:R3→R3 and is defined by, L100=110L010=201L001=101 It can be further defined as,…

Q: Let B = {v1,..., Vn} be an orthonormal basis for R". (a) Prove Parseval's Identity, that is, for any…

A: According to the given information,

Q: 59. In R4, given 2 nullspaces 1 2 00 1 V : |-1 0 -1 m 0- Find m such that dim(U n V) is max. Find…

A:

Q: Let V = P2(R), give V the inner product defined by (f,g) = Lo s(1)g(t) dt, and let W = span {1 – x}.…

A:

Q: The first four Laguerre polynomials are 1, 1 –t,2 – 4t + t², and 6 – 18t + 9t² – t3. Show that these…

A:

Q: O Given Basis tunchiono Xn- X and scalar prodnct <ti9)= foga) da ure Gram- Schmi dt precedue t find…

A: The given sequence of functions are: xn=xn The first four functions are: x1=x1, x2=x2, x3=x3 and…

Q: Let QE M,(R) be given such that the columns of Q form an orthonormal basis for R". Prove that Q'Q =…

A:

Q: Find an algebraic description of the range of A by row reducing A^T and using the relation between…

A: We know that rank(A) = rank(AT). We need to find an algebraic description of the range of A by row…

Q: - Let T : R² → R² be defined by T -E} Let u = and C = Vi = V2 = Find T(u), the image of u under T.…

A: T:ℝ2→ℝ2,Tx1x2=x1-x2x1

Q: (11) Find the dual basis {V4.V } of the stan dard basis of IR. Let T:IR → IR defined by T(xiy, z)…

A:

Q: 9. Find a basis y1 (x), y2(x) of the space of solutions to y" = y such that Y1 (0) = 1, y (0) = 0,…

A:

Q: Consider the basis 5 = {vg. Vz} for R², where v, = (1, 1) and v, = (1, 0), and let T:R? – R2 be the…

A: Here we have considered the basis S = {v1,v2} for R2, where v1=(1,1) and v2=(1,0) and T:R2→ R2 be…

Q: . Let T:M22 b IR be defined as T([e])= a + d a) Show that T is a lineur transfermation b) Find a…

A: To find kernel of T put T(X) =0 where X IA atrux from given vector space.

Q: -2 Let T : R? → R² be defined by Tx = Ax where A = Find a basis 10. B for R² such that the B-matrix…

A:

Q: Define T:R?→R? by T(x) = Ax. Find a basis B for R with the property that [T]B is diagonal. 2 - 4 A =…

A:

Q: IS Suppose that z = 0 is a regular singular point of the ODE az(x)y"+a1(x)y' +ao(x)y =0 and that ri…

A: We have to write solutions set for the given differential equation.

Q: Q1: Let L: M22 → M22be defined by L(A) 13 = |; 1|4,forAinM22. Consider the ordered basis 01 10 11…

A:

Q: What is [A]B, the coordinates of A = | 3 with respect to the standard 8 1 0 0 1 basis B of R2x2? 0 0…

A:

Q: Show that B = {1+ 2t, t – t2,t+t2} is a basis for P3. ) Let p(t) = 1+3t +t. Compute [p(t)]s- (a) (b)

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Let n >= 3 be an integer. Let Vn(x) = {[x 1 1 1 ... 1 1]T,[1 x 1 1 ... 1 1]T, [1 1 x 1 ... 1 1]T,…

A: By the consequences of vector spaces we solve the given problem.

Q: 21: Let L: M22 → M22be defined by L(A): =E [1 2j [3 4,for AinM22. Consider the ordered basis or M22.…

A:

Q: (:) - Let T : R? → R² be defined byT X2 X1 – x2 - 2 and C = 6. Let u = Vị = ,V2 = Find T(u), the…

A:

Q: Consider the basis S = {v1, v2} for R2, where v, = (1, 1) and v2 = (1, 0), and let T:R2 - R2 be the…

A: Given that basis of R2, S=11, 10 And consider linear operator T:R2→R2, Tv1=1-3 and Tv2=-61

Q: Consider P2, endowed with the following inner product: 1 1 (p, q) : G P(0)q(0) + G P(1)q(1) + for…

A:

Q: -5 1 Let y = -2 U2 = = In 4 -1 Compute the distance d from y to the plane in R spanned by uj and u2.…

A:

Q: Let V=R₂₂ [x] with (the inner product, 1 <f(x), g(x)) = f(x) g(x) dx Find a basis for the or…

A: Answer is not correct, since the second element is not orthogonal to x2+x+1. Please check and verify…

Q: onsi with its standard product. nat A E Mnxn(R) is orthogonal if and only if, for any orthonormal…

A: since {v1,...,vn} is orthonormal , thenvit * vj=0 if i different than j and 1 if i=j where I wrote…

Q: 2. Consider the basis * B = (1+*+**, x +r, 2). %3D for P2. Let p(x) = -1 + x + 2r?. Then [p(x)]R =…

A:

Q: Given: PT || QS a. Prove: APRTO AQRS R T. b. What similarity transformation maps APRT onto AQRS?

A: Corresponding angles are the angles that are formed when two parallel lines are interested by a…

Q: Let β ={x1,...,xn} be a subset of Fn containing n distinct vectors, and let B denote the element of…

A: Assume that β ={x1,...,xn}  is a basis for Fn.Let B denote the element of Mnxn (F) whose jth column…

Q: Consider the basis S= {V1, V2, V3} for R, where vV1 (1, 1, 1), v2=(1,1,0), and v3 =(1,0,0), and let…

A: Given:       Tv1=8,-1,16        Tv2=9,0,1         Tv3=-1,17,1      v1=1,1,1       v2=1,1,0…

Q: Given the bases B = {u1,uz} and B'= {u'1, u'2} for R, where %3D 1 ,U2 and u'= 1 %3D 1 The transition…

A: If the bases B={u1,u2} and B'={u'1,u'2} for R2, then the transition matrix is: PB→B'=acbd Where,…

Q: Current Attempt in Progress Let a = ci +jandb = 9i + 45j. Find c so that a and bare orthogonal. c =…

A: Given :a=ci+j and b=9i+45jTo find : The value of c so that a and b are orthogonal.

Q: 2)Let S = {[a, 0): a e R} U {(- ∞, b] : b e R} a)what would be a basis B from S? n)ls Sa subbase?

A: Given: S=[a,∞):a∈R∪(-∞, b]:b∈R To find the basis B from S and find the given family is sub base or…

Q: 1 Find a mat rix P such that P-1 1 0 0 2 0 2 1 0 O A. -10 P = OB. 1 1 P = C. 0 1 P = OD. P = O E. 1…

A:

Q: 7. Consider the basis B-{v,,Vz} for IR? where Vi =(I,1) and Vz =(-1,1). Let T:IRIR? oe a linear…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Let V = span {V1, V2}, where V1 and V2 = 1 2 Find a basis S for R3 that includes vi and v2.

A: Let V  = span { v1 , v2}  where   v1= 102 and v2 = 111 Find a basis S for R3 that includes v1 and…

Q: 7.C.1: Prove or give a counterexample: If TE£(V) is self-adjoint and there exists an orthonormal…

A:

Q: 23. Suppose R* = Span {v1, ..., V4}. Explain why {v1,..., V4} is a basis for R4.

A:

Q: O Find Hhe mahix A for T relative to the basis 8, where B' is made up of the baris vertors fand in…

A:

Q: consider the following bilinear form qp defined on IR as follows : p(x, y) x1x2 +3x1Y2 + 3x2Y1+ Y1Y2…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: Given f(x,412) = x+ 4y? +1622 9(2,412) = = =) g(X x2-1=0 F(x, y12, 1) = frayi2) + %3D f(2,412,x) =…

A:

Q: Let B={ }].OH} be basis for IR %3D Find [v]o where 6- 563

A: Given β=3-30,22-1,114 be basis for ℝ3 v=15-93 To find vβ

Q: Consider the inner product space (P1, (, )) with the inner product (p, q) = So p(x)q(x) dær. where…

A:

Q: D Consider the lineer tra given by Tlatbx+cx² lyou do not have to pro Find the folloceing a) ronge T…

A:

Q: Let T: P2 that is, 7. > P2 be the linear operator T(p(x)) = p(2x+ 1), T(co+ C,x+ C,x²) = c, + c,(2x…

A:

Q: Suppose T E L(V, W), and w1, ..., wm is a basis of range T.

A: Given that T∈L(V,W)andw1,.......wm is a basis of range T.To prove there exist…

Q: thogonal basis for W:

A: Orthogonal decomposition of vector

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.