6. If s is a scalar value and s+( xw)- ( xw) where and w are two vectors in R, then s+(6 xw)- (6 xw) is a a vector in R b. a scalar C. undefined d. a 3 by 3 matrix. Clearly explain your answer.

Q: 3. Let V = P (R) (or P(R) if 2 = 0). How many vectors does a system of linear inmependent vectors in…

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Q: c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real…

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Q: 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x? + 2y2 + 2z2 – 2xy – 2xz –…

A: Step:-1 Given quadratic form is  Q=2x2 +2y2 +2z2 -2xy -2xz -2yz Q=xyz 2-1-1-12-1-1-12 xyzQ=XTAXHere,…

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: Examine the nature of the following matrix defined by A = [0        1 + 2i       −1 + 2i      0  ]…

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Q: c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real…

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Q: [1 3 1 For the matrixP = 0 1 1 find three different vectors that are not in the column space of P.…

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Q: 1. Suppose that both sides of a system of linear equations Ax = b are multiplied by a nonzero scalar…

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Q: The four matrices Sx, Sy, S and I are defined by 0 -1 where i2-1. Show that S I and SS iS,, and…

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Q: 2. (а) Find all unit vectors orthogonal to both u = 2i – 3j + k, v = -3i + 3j + 2k If a, b, and c +…

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Q: 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x? + 2y2 + 2z2 - 2xy- 2xz -…

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A: Answer

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Q: deal with the problem of solving Ax = b when det A = 0.22.Suppose that, for a given matrix A, there…

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Q: Due to what property, applied to the matrices and scalars below, do we know that c(A + B) = cA + cB…

A: Given: We have to state which property for c(A + B) = cA + cB and (c + d)A = cA + dA

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Q: (3) If A is a real 2 by 2 matrix, A-(::) a b and a is a two-dimensional column vector, what…

A: Please check step 2 for the solution.!

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Q: If a matrix A E Mn(R) and rank(A) = n, is it true that the column vectors of A are linearly…

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Q: We now form a matrix Y consisting of the column vectors X₁, X2, X3 from question 1: -3 2 0 0 2 -3 0…

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Q: First change the given pattern into a vector w of zeros and ones by turning each shaded square into…

A: Consider the given: w=010011011

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Q: с pose the vector -6 is in the nullspace of the matrix d 6 -4 34 1 -5 23 1 -7 rmine c and d giving…

A: Topic:- application of algebra

Q: 2. Write the quadratic function f(x,,y;)=-3x; +2x,x, – 3x; – 4x, – 4x, +6 in matrix form as f(x) =…

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Q: Suppose A is equal to the following: A= 1 3 2 -1 2 -6 2 2 a) Determine N(A), the nullspace of A.…

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Q: First change the given pattern into a vector w of zeros and ones by turning each shaded square into…

A: M = 0 will be the right answer.

Q: Suppose A=QR, where Q is m×n and R is n× n. Show that if the columns of A are linearly independent,…

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Q: Express the quadratic form as v Av, where A is a symmetric matrix. x² + 3y² + 5z² - 4xy+3yz + 10xz

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Q: +0, then the matrix H = I – 2- vv7 is orthogonal and symmetric. Show that if the vector v

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Q: 10. Suppose A, B, and C are vector functions whereas 1, w, and are scalar functions, which of these…

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Q: c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real…

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Q: For A e Mnxn(C), the function ||A||. = max1<ijśn |aij| is a norm on Mnxn(C) but not a matrix norm.…

A: Matrix Norm: Let Mn×n(ℂ) be the vector space of all matrices of order n with entries in the field ℂ,…