Prove that the matrices GDCD62-62) form a basis of the complex vector space M₂(C).

Q: Let A be a 3 x 3 matrix such that B Find a non-zern vector Null(AT) -5 is a basis of Col(A).

A: Given : Let A be a 3×3 matrix and  B=5-5-2 , -54-2 be the basis of ColA To Find : A non-zero vector…

Q: Show that ?? = {(1,2,3), (−1, −1,1), (5, −4,1)} is an orthogonal basis of ℝ3, and use the Fourier…

A: Definition: A subset of a vector space V is linearly independent, if  Theorem: If is a orthogonal…

Q: Let P3 = {ao+a₁x + a₂x² + 3x³|ao, a₁, 02, 03 € R} be the vector space of polynomials of degrees at…

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Q: 3. Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the…

A: 3. Describe all solutions of  in parametric vector form, where A is row equivalent to the given…

Q: Extend the vectors [1 3 -1 -1]' and [0 -1 1 1]' to a basis for the following vector space. V = 6- 2a…

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Q: 1) Consider the basis V = (e₁, e₁+ e2, e2+ e3, e3+ e4) of F4. Find the dual basis V

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Q: If A is diagonalizable and for all eigenvalues, A of A, |A| = 1, then A is unitary.

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Q: 3. a) Determine whether the matrices A= = [ 8.B =[8]=[ 8 D= -o form a basis for the vector space…

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Q: Show M={A in M2,2| |A| =0} is not a vector space under the usual addition and scalar multiplication…

A: We will show M={A in M2,2| |A| =0} Is not vector space by exhibiting two elements A,B belongs M but…

Q: a) Let q(t) = 4t2 + 2t + 9 be an element of P2. Write the coorfinate vector of q(t) relative to…

A: We have to find the followings ; (a) We have to find the coordinate vector of  q(t) = 4t2+2t+9 with…

Q: Let P² be the vector space of all polynomials with real coefficients of degree at most 2, with the…

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Q: 127 (68) -100 -4 23 B = v= 27 is an orthogonal basis of R³. Find [v]⁄·

A: (.) Given orthogonal basis is,           and  vector (.) Orthogonal basis: A basis  is called an…

Q: Consider the vector space generated by [0, 1, –1, –1], [1,0, 2, 4], [1, 2, –4, 0]. Find an…

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Q: Find a basis for the vector space {A E R²x2 | tr(A) = 0} of 2 x 2 matrices with trace 0.…

A: Please fino the answer in the next step

Q: Let M = -6 - [31] 0 be a vector in the vector space V of 2 × 2 matrices with real number entries.…

A: (a) -3, 1, -3, 2(b) < -3, 1, -3, 2 >Explanation:

Q: Exhibit a basis for T2, the vector space of all 2 x 2 matrices of real numbers with zero trace.

A: Let V be a vector space over a field F. A set S of vectors in V is said to be a basis of V if  (i) S…

Q: a) Find an orthonormal basis of 3 [] 3} 8 W = span{ b) Find the projection onto W of the vector 1 B…

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Q: Let A be an n ×n matrix with complex entries. Prove that AA∗= I if and only if the rows of A form an…

A: Consider the given data and define all terms as,

Q: 3. Do the vectors (1, 1,0, 0), (1, -1,0,0), (0, 0, -1, 1) and (0, 0, -1, –1) form an orthogonal…

A: The solution is given as

Q: 5. Consider the space {) a a + b+c= d : 2a + b = d a + b+ 3c = 0 H = CRª. C d (a) Find a matrix A…

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Q: Which of the following sets are closed under scalar multiplication? (i) The set of all matrices in…

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Q: Expand x = (a, b, c, d) with respect to the orthogonal basis of: 2 -1 1 Vị = V2 -2 3 Express your…

A: Note: Observe that the given orthogonal basis spans only two dimension subspace of ℝ4, therefore the…

Q: 3 4 2 2. A = 1 -9 2 -6 Find an orthonormal basis of the kernel of A.

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Q: Let Tri³ ³(R) denote the vector space of all upper triangular real (33)-matrices. Find a basis and…

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Q: give an example of an infinite dimensional vector space V over complex numbers and a linear operator…

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Q: Prove that the matrices and a a a 0. a 3. a are Similar ( These 2 matrices are not deagonalısable)

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Q: Let the vectors (i, j, k) constitute an orthonormal basis. In terms of this basis, a general basis…

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Q: Let B be the basis of R2 consisting of the vectors {[2],[3]} and let C be the basis consisting of…

A: Given, two bases for : and .It is required to find the matrix  such that .To find the transition…

Q: If v is an eigenvector of A, then ū is an eigenvector of A".

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Q: 7. Prove that M2x2(C) is a complex vector space under the usual addition and scalar multiplication…

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