Explain why this statement is true: If V is a subspace of Rn, then there is a n×n matrix A such that V = Col A.

Q: Determine whether W = {a + 2x + bx²|a, b = R} is a subspace of P2.

A: Explanation of the answer is as follows

Q: Let V be the vector space of all (3×3) matrices and W be the set of all (3×3) matrices A for which…

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Q: Let A be an m × n matrix, B an n × r matrix, andC = AB. Show that N(B) is a subspace of N(C).

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Q: Find a basis of the subspace of R5 spanned by the following vectors: -7 -3 -3 + -3 7 -2 10 2 0 3 3 3…

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Q: Find the rank of the matrices where x, y, and z are distinct.

A: We have to find the rank of the matrix

Q: Show that H = : a, b eR is a subspace of M2x2(R). Hint: try to write H as the spa of a set of…

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Q: What can be said about Nul A if A is a 5×7 ​matrix? Could it be the zero​ subspace? Why or why​ not?

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Q: Let A be an n × n matrix and {v1, v2,..., vk } a linearly dependent set of vectors in Rn. Are Av1,…

A: Linear dependent: A finite non empty set of vectors v1, v2, ...vkis said to be linear dependent if…

Q: Suppose C is a linear code (i.e. subspace), and u,v are in the same coset of C. Show u+C = v+C

A: Definition A subset C⊆V(n,q) is a linear code if1) u + v ∈ C for all u, v ∈ C2) au ∈ C for all u ∈…

Q: Let W be the set of all 3 x 3 matrices whose trace is zero. Show that S is a subspace of M33.

A: Let W be the set of all 3×3 matrices whose trace is zero. Show that W is a subspace of M33.

Q: Let W be the set of all 2 x 2 symmetric matrices. Show that. W is a subspace of M2x2(R). Recall that…

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Q: Let A be an m x n matrix and let b be a vector of length n. If A x = b is consistent then rank(A) =…

A: We can check whether the given statement is true or false.

Q: Find the dimension of the subspace of all vectors in R3 whose first and third entries are equal.

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Q: Q2. Show that M2x2 , the set of all 2× 2 matrices is a vector space. Explain your answer? Good Luck!

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Q: 2. Determine which of the following is a subspace of R". (a) {(x1,x2,...X) 1 x = 0} (b) {(x1,…

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Q: Is the set of noninvertible 2 × 2 matrices a subspace of R2×2 ?

A: Given, ℝ2×2=abcd: a,b,c,d∈ℝ Let M be the set of all 2×2 noninvertible matrices  i.e.…

Q: Show that if two real symmetric matrices A, B are congruent then there is a linear change of…

A: The objective of this question is to prove that if two real symmetric matrices A and B are…

Q: Let W be the subspace of M10,10 (i.e., 10 × 10 matrices) consisting of all matrices whose diagonal…

A: A basis B for a vector space V is a linearly independent subset of V that generates V.  The number…

Q: Suppose B is a 5 x 5 matrix and Nul B is NOT the zero subspace. Do you have enough information to…

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Q: Let A be an m×n matrix. Find all b such that the set of solutions to Ax = b is a subspace and prove.

A: Given: Let A be an m×n matrix.  The objective is to find that the set of solutions to Ax =b is a…

Q: Let M be the set of all 2 ×2 matrices of the form | a a2 | | b b2 | Is M a subspace of the…

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Q: Show whether the set W of all diagonal 3 x 3 matrices is a subspace of or

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Q: Find a basis of the subspace of R5 spanned by the following vectors: 4 1 -1 8 6 6 -2 2 12 16 -1 -2 2…

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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.