Find the cosine of the angle between the vectors P1(x) = 1 + 2x – x² and p2(x) = -1 – 3x + 2r² with respect to the standard inner product on P2. O None 102

Q: would the two vectors be (1 1 1 0) and then (0 0 0 1)?

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A: Given: Inner product p,q=a0b0+a1b1+a2b2

Q: 2 Find The vector normal to The vector A=2i-3j Ans/ N= 3i+2j

A: Suppose, the vector normal to A = 2i - 3j is, N = ai + bj

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Q: Find the magnitude R and direction 0 of the resultant vectors. 7.0N 5.0N 5.0N 6.0N 2.5N 80 20 30 10…

A: if you find my answer helpful please put thumbs up. thank you. the required solution is given below…

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A: We have to find the ratio

Q: +5 c) Let y = n44| and u = is Span{u} and one orthogonal to u. where n=9. "t. Write y as sum of two…

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Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Determine the length of each vector.

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Q: Let V=R^2 and let H be the subset of V of all points on the line 2x+3y=6. does H contain the zero…

A: Given  V=R2 and let H be the subset of V of all points on the line 2x+3y=6.

Q: 5. (a) Find two vectors of norm 1 that are orthogonal to the vectors u = (5) and pue (4 E)=

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Q: The vector sum v1i + v2 j is a ________ ________ of the vectors i and j, and the scalars v1 and…

A: The vector sum v1i + v2 j is a linear combination of the vectors i and j, and the scalars v1 and v2…

Q: Find all value(s) of t such that the vectors 2t i – 2 j– k and 2ti+ 3t j – 2k are nernendicular

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Q: Decompose the vector v=3i+2j into two vectors v1 and v2, where v1 is parallel to w=2i+j, and v2 is…

A: Decompose v into two vectors v1 and v2,where v1 is parallel to w and v2 is orthogonal to w.v=3i+2j,…

Q: Find all vectors in R* that are orthogonal to both 1 1 V1 = and V2 2 -2

A: Linear Algebra: The vectors are: v1=112-2v2=2112Let denote the vector v3=v1v2v3v4

Q: 12. Let A = ( d ef g h Find the column vector B such that AB =

A: Let A be a square matrix. Use the following formulae, to obtain the required result.

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Q: Find the value of y in ( 3x + 4yi)(6 -7i) = 3 + 5i  A. 1/20 c. 1/10  B. 3/20 d. -1/15   Q2: If…

A: We have to find the value of y.

Q: -2 [5a] Find the value of a such that the vectors u =a +4 and v = |2 are orthogonal.

A: Please refer the attached image for complete solution. Given: u = -2a+4   1  & v = 5a 2 0 are…

Q: d) Prove that ||vxw||²+|v-w[? = ||v||²|w||² for all vectors v, w in R3

A: Prove the following

Q: Find bases for the spans of th e vectors in the given exercises from among the vectors themselves.[2…

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Q: Given v = - 3i + 5j and w = i+j, a. Find projwv. b. Decompose v into two vectors V1 and V2, where V1…

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Q: Consider the inner product on R2 defined by ((x, x2), (y, y2)) = x11 + 4x2y2. Which of the following…

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Q: Q2] (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

A: (A)Consider the given information.Let the ball is defined by the sphere and the equation with radius…

Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: we have to find projwv of the given vectors and then we have to decompose v into two vectors, v1 and…

Q: Find the possible values of x if vectors are j +2k, v =2i + j –- k and w = xi+j - k coplanar: u = i…

A: Given vectors are u=i-j+2k, v=2i+j-k and w=xi+j-k. To find the possible values of x if vectors are…

Q: . Prove that for any two vectors d and b in R³, there exist two vectors bí and b such that: T = 6 +…

A: The vectors a→ and b→ lie in the 3 dimesional axes.Any vector is a sume of two vectors.Thus,…

Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: we have to find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

Q: Find the cosine of the angle between the vectors P1(x) = 1 + 2x – x² and p2(x) = 2 – 3x – 2x² with…

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Q: Find the cosine of the angle between the vectors P1 (x) = 1 + 2xr – x² and p2 (x) = -2 – 3x + 2x² -…

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Q: Use the inner product (p, q) = aobo + a¡b1 + azb2 to find (p, q), ||P||, ||g||, and d(p, q) for the…

A: Given polynomials are: p(x) = 3 - x + 2x^2 q(x) = x - x^2 We know that the inner product is given…

Q: Let a = (5, 4) and b = (1, –5). Show that there are scalars s and t so that sa + tb = (-13,-22) You…

A: Given, Let a=5,4,b=1,-5 And sa+tb=-13,-22

Q: Find the triple scalar product (u xv) •w of the given vectors. u= - 5i – 3j + 4k v = 9i – 10j + 7k w…

A: Given that      u = -5i-3j+4k     v = 9i-10j+7k     w = 9i-7j-3k Here we have to find the value of…

Q: Set a = 0 gives Uo = {(x1,x2, x3)T E R³|x1 + 2x2 = 0}. Define an operation O for the vectors in R3…

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Q: Find a so that the vectors v = i- aj and w = - 9i - 8j are orthogonal. (Type an integer or a…

A: As we know that; If two vectors v & w are orthogonal to each other then the dot product or…

Q: The dot product ol tWU veciurs Y1 Y2 and y = Yn in R" is defined by a· j = x1yh + x2y2 +... + x„Yn.…

A: Given: x=8-83 We need to find a vector y such that x.y=0. This can be done as follows:

Q: 98 25) Gvon vectors v= 30tj and w=-2i -j. Decompose v into two vectors V, and Vz, where V, is…

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Q: Find the best approximation to z by vectors of the form cv1 + ¢2V2. 3 1 -7 -1 1 V1 V2 -3 3

A: To find  The best approximation to z by vectors of the form c1v1+c2v2.

Q: Find the cosine of the angle between the vectors P1 (x) = 1 + 2x – x2 and p2 (x) = -2 3x + 2x? %3D -…

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Q: (5) Find the cross-product ū x i of each of the following pairs of vectors; (i) ū = 2î + ĵ + k; i=…

A: Solution: (i) u→=2i^+j^+k^,  v→=8i^+2j^+2k^ Now, u→×v→=i^j^k^211822           =1122i^-2182j^+2182k^…

Q: b/Let u and v be a nonzero vectors in 3- space, and let e be the angle between these vectors when…

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Q: One of the following vectors lies in span{ 2+ x +x², 3+x – 2x? } (A) 3 + 2x + 4x² (B) 3 + 2x + 5x?…

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Q: Find Q for the QR factorization of A Ex: 1.23 02 0.given the orthogonal vectors 4 ------ 0.83 1.67…

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Q: When decomposing the vector into the sum of two vectors, the first is parallel to the vector A = 2i…

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Q: s such that vectors –si – 2j+5sk and 9si +j+3sk are orthogonal.

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Q: Use the standard inner product on R" to determine if the vectors or functions are orthogonal. 2 -3 1…

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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.