Determine whether or not the following matrix is orthogonal. Justify the response.   Q = 1/√6  (√3     1      √2)                    0     -2     √2                   -√3    1    √2

Q: Determine if the columns of the matrix A = - 2 1 4 0 84 4 t 0 are linearly independent.

A: Here we need to show that columns of matrix A are linearly dependent or independent.We all know that…

Q: Find the matrix of the quadratic form. Assume x is in R?. a. 3x - 8x,x2 + 2x3 b. 5x, + 18x,x2

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Q: Determine whether the matrix -1 -1 -4 A -8 -3 -16 1 7 is diagonalizable. If A is diagonalizable,…

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Q: [2 -1 1] A = |1 1 2,x = |y| and b = |b2 [-1 5 4] a. Determine if the columns of the matrix A span…

A: We have to determine  whether the column of matrix A can span R^3

Q: Find the value of the vector product XY using the matrices below where p = 9 and q = 6: X = p -1 q…

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Q: Let A be a m x 3 matrix with columns V₁, V2, V3. Find A0, A (-0. and A 0

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Q: [2 3 4 A = 13 | من بن 2]

A: Tje solution is given in the next step.

Q: 3 Compute x using the vectors w = -4 and x = 2 - 5 2 x = (Simplify your answer. Type an integer or…

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Q: Let x1, x2, x3, and b be the column matrices.Find constants a, b, and c such that ax1 + bx2 + cx3 =…

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Q: Find out the pivots of the following matrix and comment whether it is singular or not. 2 0 0 1 10 0…

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Q: Find the matrix of the quadratic form. Assume x is in R³. a. 2x² +8x² − 3x²3 - 10x₁ x₂ + 8x₁×3 −…

A: Concept

Q: Let A be a 4×5 matrix with 4 pivots. Do the columns of A span R4? Do they span R5? Justify your…

A: As A is a 4 x 5 matrix with 4 pivots so, it has a pivot in its every row. So, yes the columns of A…

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: Express the quadratic form (c₁x₁ + C₂X₂ + ... + Сnn)² in the matrix notation TA, where A is…

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Q: 1 Find the linear combination 2$1 +382 + 4s3 b. Then write b as a matrix-vector multiplication Sx.…

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Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists)

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Q: Use the definition of Ax to write the vector equation as a matrix equation. X₁ 4 6 -9 +x2 2 -3 The…

A: Given- The vector equation is: x146−91+x2−2−329+x38430=9147             ......1. To find- Write the…

Q: () Write the statement of Cayley-Hamilton theorem for square matrices.

A: Cayley-Hamilton statement

Q: Let V = [- 7, – 7,0] and V½ = [0, 3, – 4]. Use the Gram- | Schmidt procedure to construct an ordered…

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Q: Given the matrices A and B, calculate [A, B]. 6+ 3i B = 7 9 i A = 3+i 2-i +i 4 a11 a12 [A, B] = a21…

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Q: Compute the third row of the product (if it exists) by summing an appropriate linear combination of…

A: To Find : Third row of the Product of given matrices.

Q: -3 -1 Find all a so that the matrix A = 1 -1 is positive -1 4

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Q: Re-order the equations, so that the coefficient matrix is diagonally dominant.

A: Writing Co-efficient matrix of given system of equations: [0 1 0 4 -2] [1 0 3 -1 0] [4 0 1 0 1] [2…

Q: A = 1 0 1 2 1 41-2 34 2 2 1 -1 2 21 -1. LO 10

A: The solution is given as

Q: Find the inverse of the matrix A, if it exists. A 02 -407 0 2 0

A: I have explained everything with in the solution. Please go through that.

Q: Express Ac as a linear combination of the columns of A.

A: Given A=2-34-1235-1-2   C=214

Q: Can you find the A (matrix) for the following? Can you use the transpose properties, such as taking…

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Q: TRUE OR FALSE a. If AB = [0], then A or B is a zero matrix.  b. For a square matrix A,AAT = ATA.…

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Q: A. Construct a 2 × 2 matrix that is invertible but not diagonalizable. Also provide the inverse of…

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Q: Find matrix A, given that: :) 8. -2 2A-1 10 9.

A: NOTE: Refresh your page if you can't see any equations. . divide both sides by 2 take inverse on…

Q: Consider the square matrix below: 2 -4 A = 3 2 O -2 Use Doolittle's method, expressed the given…

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Q: . List 2 matrices that com Make the vector ५ (7) a unit vector,

A: (i) We have to given example of two matrices which commute with all other n×n matrices. (ii) We have…