Prove that H is a subring with unity of M2x2(ℤ), under the usual matrix addition and matrix multiplication.

Q: Prove using elements that for any square matrices A,B of the same size and constant K.…

A: For any square matrices A,B of the same size and constant K.  tr(kA+B)=ktr(A)+tr(B)

Q: If A and B are arbitrary real m X n matrices, then the mapping (A, B) = trace(A" B) defines an inner…

A:

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: Let A be an (m n) matrix then nullity(A) + rank(A) = = m. False O True

A: The objective is to find true or false of the above statements.

Q: Let M2x2 (R) be the set of all 2 x2 commutative and invertible matrices with real entries. Does M2x2…

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Q: Consider the following matrices A, B and C (attached in image). Note that only the entries of matrix…

A: Since there are more than one questions, so find the solution of the first question.

Q: Suppose that A = PDP-1, where P = A¹ = 100 -1 1 -1 0 -1 0 Use the diagonalization of A to compute…

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Q: 9. Show that the matrices (6) 65), (8), and (1) generate M2×2(F).

A: We have to show that the matrix  and  generate

Q: 22 Change I into A¬1 as you reduce A to I (by row operations): 1 3 1 [A I] = 1 4 1 0 and [A I]= 3 9…

A: [A I] =>[I A-1]

Q: Identify the row operation that will transform the matrix 8 -9 6 1 19-50 [¹1₁ -1 4 -8 B into -1 4 -8…

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Q: 4. Let M (for matrices) be the set of all 2 x 2 matrices over the reals and x, y ∈AM. Does…

A: This statement is not true.

Q: sider the following matrices A, B and C (I have attached an image). Note that only the entries of…

A: As per the guidelines I am answering first question with all its parts.(Note that first three parts…

Q: Consider the quadratic polynomial q(x) = 2x + 8x1x2 – 8x – 3x1 – 3x2 + 3. - - Find the symmetric…

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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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Q: For the system (M2(R), *), demonstrate or explain why: i. (M2(R), *) is closed ii. (M2(R), *) is…

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Q: Suppose u1, ... , Un and v1, ... , Vn are orthonormal bases for Rn. Construct the matrixA=UI:VT that…

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Q: 9. Show that the matrices ( ) ( ) (19). generate M₂×2(F). and (689)

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Q: Show that a matrix B has a left inverse if and only if BT has a right inverse.

A: Let’s assume that C is a left inverse of matrix B i.e.