7 Find w if (w)s = |0| relative to the basis S = 3 – 10 3 W =

Q: Find a basis of ker T. T: M22 → 1 M22; T( x ) = AX, where A = 0 0 O[1 0 0 1 0 1 1 0 1 0 1 0 0 -1 0…

A: The transformation T:M22→M22; T(x)=AX, where A=1100. We have to find the basis of kerT.

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: D) How do you know that T: P3> P2? (How do you know that the codomain is correct?) E) Find T(x + 2x?…

A: Given, T(p(x))=p'(x)-xp"(x) (D) p(x)∈P3⇒p(x) is a polynomial at most of degree 3. ⇒p'(x) is a…

Q: (d) Find an orthonormal basis for V = im(A). (Hint: If you find that the numbers aren't working out…

A:

Q: 26. B = (f1, f2, f3) is a basis for R2[x]. If the change of basis matrix 1 3 from B to Sr, læ] is 1…

A:

Q: 7. Prove that p, (t) = 1+t², p2(t) = t – 3t2, p3(t) = 1 +t – 3t, is a basis for P2.

A:

Q: -2 Let y = what are the expansion coefficients of y in the basis {vo, V1, V2 , v3 } you found in the…

A:

Q: 25. B = (f1, f2, f3) is a basis for R2[x] where fi = 1+ x + 2x², f2 = 1 + 2x + 5x², f3 = 2 + x +…

A:

Q: -6 Express the general solution of Ax =b where A = and 6 -12 -6 as x = x, + cx„ where x, is the row…

A: Given: Matrix A=3-66-12 and B=-6-12. The objective is to express the general solution of Ax=b.

Q: Explain why S is not a basis for P2.S = {−3 + 6x, 3x2, 1 − 2x − x2}

A:

Q: XI Let W = X2| 0 2X1 -X z+ X4= + Xy = o] be a subset of Rt IRt. which one is the basis for W?

A: Given W=x1x2x3x4:2x1-x2+x4=0 be a subspace of ℝ4

Q: 2) Let T(a+bx+cx² + dx³) = i) A basis for Ker(T) would be: ii) The Nullity of T is: iii) The Rank of…

A: As per our guidelines only first Question is solved. To get solution of remaining question kindly…

Q: XI Let 2 Xi - X z+ Xq = oY be a %3D Xu subset of IR4. which one is the basis for W?

A:

Q: 1 0 0\ 1 0 0 0 0 0 0 0 0 0 0, Find a basis of P3, where the matrix of D equals No justification is…

A:

Q: Suppose A E R4×3 has the following QR factorization A QR V2 -V2 [1 0 1 0 0 0 0 -1 1 1 1 -1 R = 1…

A: We will first find the matrix A using the QR factorization given.…

Q: The coordinates of p(x)=5+3x+x² relative to the basis {1+x,2-x2,3+x+x²} is O (-1,1,2) none (0,1,1) O…

A:

Q: EX ample (12.1) Find the Singular Value De composiion of A= 0 4 3 4 00 3 00 Solution: FInd Q2…

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Q: -2 9 Consider the matrix A = Find a basis B -1 4 of R2 such that the B-matrix B of T (x) = Ax is 1 1…

A:

Q: Q2) Find the basis for Col A and a basis for Null A and state the ranks of a matrix A and state the…

A: Solution: The objective is to find the basis for column space and null space

Q: (4) 10. Let H = {r+2x2, 1+ ka?, k + (2k + 3)r2} (a) For what value(s) of k is H linearly dependent?…

A: This belong to linear algebra.we check linear independence for the given vectors and find k so that…

Q: b) Find a basis for W. c) What is the dim(W)?

A: You want solution for part B and c, So I have given only part B and c. Basis (definition) Subset B…

Q: 5 Find w if (w)s = |0| relative to the basis S = {-3 -5 2 } 2 3 w =

A:

Q: 6.4 H 6 Suppose A is Hhe matia for T: R²→R relative to the standand basis. Find the velative to the…

A: Consider the matrix A and basis B’.

Q: (b) Calculate a basis C for S and state dim(S).

A:

Q: 2. Let L: R3 → R³ and let 1 1 [L] = 3 -2 1 0 3 be the matrix of L with respect to the standard basis…

A:

Q: For the following LP, the optimal basis is {x2, S2}. Find the optimal table. max z = x1 + 4x2 S.t.…

A: Given that the LPP is  max z=x1+4x2x1+2x2≤62x1+x2≤8x1,x2≥0 Rewrite the LPP after introducing the…

Q: Let S = (2x, 1 - x, x2 +x 1,x+ 1}. Then PA P1 O sis a basis for the nbove Sis a basis for the above…

A:

Q: S = (1 + x, 1 – 2x) is not a basis for P,(the space of polynomials of degree less than 2) Select…

A: False.

Q: 1.14 If r(t) = (312-4)i+j+(+3)k, whcre (i. j. k) is a constant standard basis, find i and F. Deduce…

A: Since you have asked multiple questions. So, we are solving only 1 for you. If you want more…

Q: B = (f1, f2, f3) is a basis for R2[] where fi = 1+ 2x + a², f2 = 2+ 3r + 2x², f3 = 2 + x +3x². If…

A: The correct option is option (e) 1 + 2x²   The detailed solution is as follows below:

Q: b) Let v1 = (1,2,1), V2 = (2,9,0) and vV3 = (3,3,4). Show that S = (V1, V2, V3) is a basis for R³.…

A: Explained below...

Q: 6. Find a polynomial p(x) for which {r² – 1, x² +x +2, p(x)} is a basis of P2(R).

A:

Q: What is [p]B, the coordinates of p = 4+ 7x with respect to the standard basis B = {1, x} of P1? Ex:…

A:

Q: Suppose A E R4×3 has the following QR factorization A = = QR V2 1 -1 1 |1 -1 V2 -V2 [1 1 0 1 -1 0 0…

A: Here, we need to find an orthonormal basis of A. First we will row reduce A to find the column basis…

Q: [3 9 5 : A=0 4 0 1 00 0 0J Find a basis for the null space of the matrix.

A:

Q: is linearly independent. spans R3 5 is a basis for R³. None of the above.

A: Given set of vectors are : S=003.1,-2.74.90,-2.74.93.1 in R3 Now need to select which statements are…

Q: Prove that P-1 = P" if and only if the columns of P for an orthonormal basis for R" for P n n.

A: We have to prove that P−1=PT if and only if the column of P for an orthonormal basis for Rn for…

Q: 3. T: P, P, is defined by T(a, + a,x) = -a, + (a, + a,) B is the standard basis for P1, and B' =…

A:

Q: s = (6 4 1) (3 −5 1) (8 13 6) (0 6 9) explain why S is not a basis for R3

A: Given S=6,4,1,3,−5,1,8,13,6,0,6,9. We have to explain why S is not basis of R3. Definition:- The…

Q: B = (f1, f2; f3) is a basis for R2[r] where fi = 1+z+2r², f2 = 1+2r + 5x², f3 = 2+1+2r². If g e…

A: Coefficient of linear combination is given. We have to find the element

Q: 12. Let B = {1+2x, x – x², x + x²}. (a) Show that B is a basis for P2. (b) Let p(x) =1+3x + x².…

A:

Q: Explain why S is not a basis for P2.S = {1 + x2, 1 − x2}

A: Given: S = {1 + x2, 1 − x2}

Q: Let S = {v1, v2, v3} and T = 1 2 be ordered basis for %3D 2 | -2 1 -1 R³. If the transition matrix…

A: Given the ordered basis for R3, T=-112,-121,2-1-1 & S=v1,v2,v3. The transition matrix from the…

Q: 1 2 1 1 Let U1 = 1 U2 = 1 V3 V4 1 1 t For what of value of t is the set{v1, v2, V3, v4 NOT a basis…

A:

Q: a b 1) Let T cla + 2b + 1c + 3d + (-11) e+ (-la+ (-1) b + (-2) c + Od + 7e) x. d to Then a basis for…

A: The given transformation is  Tabcde=1a+2b+1c+3d+-11e+-1a+-1b+-2c+0d+7ex To find a basis for KerT⊥.

Q: Consider the limear thans femartin IC) - Ax de fiva by te matrix Ac 20 23 1 34 2 2 2. 1 20 D Find a…

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Q: S = (1+ x, 1- 2x) is not a basis for P,(th

A:

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.