18 Given the basis B -2 1 7 7 if the coordinates of w relative to basis B are wB - 4 find w 2

Q: The set B= {2+z, 6+3z + 3z,- (23+9z + 12z*)} is a basis for P Find the coordinates of p(z) = - (73 +…

A: Coordinates

Q: If B={(1,1,1).(1,0,1),(0,1, 1) } is a basis of R3, then the second coordinate of the vector (3.5.7)…

A: On solving this we will get

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

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Q: 1 3 S = 4 9. a basis for R3? Explain why or why not.

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Q: 5. Which one of the following sets of vectors is a basis for R B C D. 8.

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Q: Given the ordered basis 4 B = U2 = 5 U3 = -8 -3 7 -33 find [v]B, the coordinates of v = 57 with…

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Q: } 4. You are given that B = {1– 2x + x?, x+ x?, 2 +x – a?} is a basis for P2. (i) Find the…

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Q: Let V = P2(R). Show that 3 = {1+r+2²,x+r², x²} is a basis for V. [You may assume that we already…

A: We will use the fact that if DimV =3, then any subset of P2(R) consisting of three linearly…

Q: Given the basis B 1 5 if the coordinates of w relative to basis B are [w]B find w

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Q: Given the ordered basis 5 7 1 B = A1 3 0 -6 -8 -5 -2 3 Аз -7 45 find [A]B, the coordinates of A : 4…

A: The objective is to find the coordinates of A with respect to the given basis.

Q: Given the basis B = 18 if the coordinates of w relative to basis B are wR = -3 find w %3D W = > Next…

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Q: The set B = {4x? - 1, z -3+ 12z2, 12 – 3x 40x} is a basis for P2. Find the coordinates of p(x) = 52…

A: write each polynomial as a vector  4x2-1=x2x140-1 12x2+x-3=x2x1121-3 -40x2-3x+12=x2x1-40-312 write…

Q: Given the ordered basis -1 -8 A1 = -5 , A2 -3 3 4 A4 -5 -5 -3 A3 -1 7 44 22 with respect to B. 3…

A: According to question given :-A1=96-5-3, A2=-1-830, A3=-54-1-4, A4=-5-367The coordinate of A…

Q: prelative to the basis S=(P. P2. P3) for P2. p = 20 - 30x +25x; P, = 5, p, = 5x, ps = 5x. %3D %3D…

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Q: The set B = {2 – 4x?, 8+ 3x – 16x2, 21 + 9x – 40x²} is a basis for P2. Find the coordinates of p(x)…

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Q: B = (f1, f2; f3) is a basis for R2[r]. If (1 2 1) is the change of basis 1 1 2 matrix from Saae to B…

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Q: Lemma 2.8 B is a basis of T iff VO ET 3 BO CB : 0 =UBo Proof: excercises.

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Q: –10 S = l2] ] 13 2. 2.

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Q: 11. For what value(s) of k does the following set of vectors form a basis for R³? ·4·0 3 3

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Q: Determine whether S is a basis for P3. S= {5 – 3t2 + t3, -4 + O is a basis of P3. t2, 3t + t?, 5t}…

A: Given S = 5 - 3t2 + t3, -4 + t2, 3t + t3, 5t

Q: За + 6b — с ба — 26 — 2с - Find a basis for H = : а, b, с €R -9a + 56 + 3c | -3a + b+ c

A: Given H=3a+6b−c6a−2b−2c−9a+5b+3c−3a+b+c:a,b,c∈R We have to find the basis for H. First write the…

Q: Find all values of a for which {[a? 0 1]. [0 a 2].[1 0 1]} is a basis for R3.

A: let v1=a2 0 1 , v2=0 a 2 and v3=1 0 1 be the three vectors in R3. now these vectors forms a basis of…

Q: -{)--- 00 1 1 Let vi = 1 2 and set 3 V2 = 1 4 V = {x € R* : x · vị = x · V2 = b1 = 0}. If a2 b2 is a…

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Q: 1 31 3. Let S = }|2 [3. 3 2 a. Is span(S)=R³? b. Determine whether S is the basis of R³.

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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 =

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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: 9) a) Find the standard coordinate basis for the and B1 = = B -1 b) What is the coordinate basis of…

A: (b) Given :- The coordinate basis of xy in the basis B2 = -1420

Q: 17 37 Consider the orthogonal basis B = -3 10 of R³. -3 1 -9 11] Let V = -16 7 а If vB= |b|, what is…

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Q: Suppose S= {Pi;P2•P3;P4,P5;P6} is a basis for P5 and p is a polynomial of degree 4. Then the…

A: Given The coordinate vector is a vector in which each component is the coefficient of the linear…

Q: Given the ordered basis -1 -5 A2 -4 1 6. | B A1 %3D %3D -2 -3 5 6. -2 A4 9 -2 Аз 6 2 -9 -4 with…

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Q: The set -4 -4 B = -6, [. is a basis for R². Find the coordinates of the vector x = relative to the…

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Q: Given the ordered basis 5 3 -9 B = { A1 A2 -1 8 4 -1 ,A4 -7 Аз -3 -4 -5 32 -28 find [A]B, the…

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Q: 1 2 1 251 1 3 7 2 2 4 9 3 - Given A = 1 Find the basis for nullspace of A. HA 3 3. 1 a. b. С. d. 1…

A: A=121025113722493-1

Q: See picture

A: Does the set L of two vectors form a basis for the subspace S?

Q: Let B= { }],}} 3 -3 2 2 -1 be basis for IR Find [v]a where 15 6- 3.

A: Find the determinant of vectors of B to check linear independent. We have to Express v as a linear…

Q: a The vector b can be expressed in the basis с 0 0 CHEED-E- -2 -2 -3 as What is -3 -4 0 -2 the…

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Q: [2 1 1 V2 = 3 1 V4 1 Let Vj = , V3 1 4 1 2 8 For what value of t is the set {v1, V2, V3, V4} NOT a…

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Q: = {W₁, W2, W3} is a basis for R³, where 1 3 H W2 = 3 W3 -2 -4 Determine if the set B W₁ = 2 9 = -3 A

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Q: 10. The solution set to the equation Ax = b is 1+t1 2 - t t + u :t, ueR} when b %3D L2t· - u a) How…

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Q: 1 3 Let A = -1 -2. Find a basis for Col(A)+. -3 16 A basis is {v1} where V1 =

A: Given is a matrix A. To find: Basis for perp of Col(A)   First we find Col(A) from the given matrix…

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) Find q if S is the basis in x2 + 1, x2 – 1, 2x – 1. (c) Find B if S is the basis in 3 -1 -12 1 В…

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Q: 10 2 1 4 5. Let A= 1 130 4 10 20 3 • What is RREF(A)? o Find a basis for R(A). • Find a basis for…

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Q: 3. 1 V=R , cat d2= d3=1 1. 2. Tet it be Shaw that basis. Find the Ed1,22,233 in V is a Dual bose at…

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Q: [7 2 4 6 What is [A]B, the coordinates of A = with respect to the standard 10 0 1 basis B = of R2x2?…

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Q: Given the ordered basis 4 0 -3 6 Az = -4 6 8 -5 Az = 3 9 A4 = -7 -8 -3 find [A]g, the coordinates of…

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Q: 1. Use coordinate vectors to show that (4-t), (3-1), 2-t,and 1+5t-6r +f form a basis for P. Then…

A: To check that the polynomials 4-t3, 3-t2, 2-t, 1+5t-6t2+t3 form a basis for P3. We will write the…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.