47. The 4 by 4 Hadamard matrix is entirely +1 and −1: 1 1 1 −1 1 −1 1 -1 −1 1 154 H= = 1 1 Chapter 2 Vector Spaces Find H¯¹ and write v = (7,5,3,1) as a combination of the columns of H.

Q: Find a formula in terms of k for the entries of Ak, where A is the diagonalizable matrix below and…

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Q: -5 10 5 Let A = 2 -3 -1 and b = -2 -1 4 0 Denote the columns of A by a1. a2. a3, and let W = span…

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Q: [-5 -5 [-3] 1. For the matrix A 2 -3 determine (and explain why) if vector ú 3 is | 4 2 3 2 a. in…

A: GIVEN A=-5-5002-3423 to determine if vector u→=-332

Q: Write the dot product of (1, 4, 5) and (x, y, z) as a matrix multiplication Ax. The matrix A has one…

A: Given, A=145, x=xyz Ax=0

Q: B = %3D 0 -4 2 -8 1 2 -3 7 3 -1 -2 -8 -1 20. Can every vector in R* be written as a linear…

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Q: If Y and Y are the first and last column vectors in the inverse of a [1 -1 2] matrix A = 0 3 2 then…

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Q: Find a general solution of the equation: 5xy' = 2 – y %3D

A: Please find attachment for the details solution

Q: 19. Can each vector in R4 be written as a linear combination of the columns of the matrix A above?…

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Q: 3 2 . B = 3 and C =-1 For the Matrices A= 1 4 Find: (AT.B)+ 2 C

A: Given that, We have to find, Then we get, AT=1-32140…

Q: Consider the matrices A and B presented below. Find the following matrix products: AB= BA= A² = B² =…

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Q: Let 3] A = -2 1 B = 3 If possible, compute the following. If an answer does not exist, enter DNE. AB…

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Q: Let y = 1 2 and u= 4 2 Write y as the sum of a vector in Span (u) and a vector orthogonal to u.…

A: Introduction: The projection of a vector onto another vector is the application of dot product. This…

Q: Write 2x + 3y + z + 5t = 8 as a matrix A (how many rows?) multiplying the column vector x = (x, y,…

A: Given: Equation is Objective:Represent the equation in matrix form, , where  is the coefficient…

Q: To determine whether a set of n vectors from R" is independent, we can form a matrix A whose columns…

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Q: If A-[1 2 3;4 5 6;7 8 9] 1-set the value (1,2,3} for the fourth column 2-The number 4 multiple…

A: See answer below

Q: do

A: As per our guidelines only first three sub questions are solved. For remaining sub questions kindly…

Q: 3. Let [1 2 3 A = |4 5 6 7 8 9 (a) What is Aēj? Present it as a linear combination of the columns of…

A: Given

Q: The matrix X1 X = is called a vector.

A: We have to find

Q: 1 3 3 1 3 -2 2 -1 -1 -1 0 -4 1 1 1 -5 A = B = 2 -8 1 2 -3 7 - 3 -1 -2 -8 2 -1 20. Can every vector…

A: As we know basis of the column space of matrix B is formed by columns of B that correspond to the…

Q: 39. CHALLENGE Tell whether each of the following situations involving three planes is possible. If a…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the transpose, conjugate and tranjugate of the following matrices: # = √² = 3₁ 2 AT = 1-1 31 7…

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Q: Let A be an m x n matrix and let b and c be column vectors with n components. Express the dot…

A: Answer :

Q: In the inner product space of 2-square matrices, with the inner product <uv2 trlu the two matrices…

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Q: Write y as the sum of a vector

A: Given,   And

Q: a. Express each column vector of AB as a linear combination of the column vectors of A. b. Express…

A: a. To express each column vector of AB as a linear combination of the column vectors of A, we can…

Q: Q1/ If 1 4 -3' -3 8Y 2 -3 -6,B = 1 1 and C = 2 11 -2 6. -3 are three matrices find |D"| where D = A?…

A: The given matrices are: A=1042-3-6902 ;       B=30-30111-26    and     C=0-38021-301

Q: -3 -3 9. 2 Let A = -3 -6 12 and b = 3 -3 -2 13 -5 Denote the columns of A by a1, a2, a3, and let W =…

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Q: 4 Compute x using the vectors w = -2 and x = (Simplify your answer. Type an integer or simplified…

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Q: Use the definition of Ax to write the vector equation as a matrix equation -2 + Z2 - 5 3 +Z4 2 4 Z1…

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