Give an example where the statement: If U and V are vector subspaces of Rn, then U ∪ V is also a vector subspace of Rn. holds true.   Note that this will hold true if U is a subset of V or vice versa. Kindly give an example for R2. I would prefer if the example is in matrix form.

Q: Let a,, a, , b €R³ and suppose that the vector equation x,a, + x,a2= b has a solution. Then, which…

A: The given expression implies that b can be written as linear combination of a1 and a2.

Q: 1. Let W be the set of matrices in M2.2 given by W 3 -20 (a) Determine whether W is linearly…

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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: For Exercise, determine the inverse of the given matrix if possible. Otherwise state that the matrix…

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Q: Find the dimension of the vector space.R3m

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Q: Let A be a real 2 x 2 matrix satisfying A? - 4A = 0, where O is the zero matrix. SKIP Find the…

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Q: a Let A = b - a then A is diagonalizable. b Select one: O True O False

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Q: Let A and B be invertible 5-square matrices such that A| = 4 and B = 2. Then |2A. B 2 %3D

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Q: Let A = [ 9-8 4-3 Find an invertible matrix X such that X-¹AX is diagonal.

A: Introduction: A matrix A of dimension n x n is called invertible if and only if there exists…

Q: X = 4 1 -3 0 0 6 1 2 -12 10 -1 = [X₁ 5 X2 X3 X4]

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Q: 1. Let W be the set of matrices in M22 given by {E 2 W = 3 -20 0 (a) Determine whether W is linearly…

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Q: 6. An n x n matrix A is diagonalizable if and only if it has n distinct eigenvalues. ? 7. Let W be a…

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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: Let A and B be two square matrices. Assume that both A and B are invertible. Show that BA is…

A: Note that--- If determinant of a matrix is non-zero then the matrix is said to be invertible and if…

Q: 5а+ 2b Decide whether the set of all vectors of the form is a subspace of R³ or a

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Q: a 12 Let A 0 a 1 For what value of a is A diagonalizable? Explain your 00 a answer.

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Q: ={b₁,b2} and C= {C₁,C₂} be bases for a vector space V, and suppose b₁ 1 Let B= a. Find the…

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Q: Find the matrix M of the linear transformation T : R³ → R² given by - (E) 6x1+ x2+ (-5)æz 8x1+ 3x3 M…

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Q: Given the following vector X, find a non-zero square matrix A such that AX=0: You can resize a…

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Q: Determine whether the following matrix is diagonalizable or not. If yes, diagonalize it; if not,…

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Q: Let V₁ = [], , V3 Determine if the set {V₁, V₂, V3} is linearly independent. ‚ V2 =

A: Definition of linearly independent set

Q: X + x, + 3x, = 0 Given this system of equations: 2x, + x, +4x, = 1 3x, + x, +5x, = 2 %3D a. Find the…

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Q: X = 4 0 1 0 -3 6 1 2 -12 10 -1 = [X₁ X₂ X3 X4] 5

A: Linear algebra

Q: find if the vector x is in the range for matrix A

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Q: 27. For any matrices A and B for which the product AB is defined, the (i,j)-entry of AB equals a¡bj…

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