For matrices in M,, (K) for a field K, which of the following is true (a) the product of two such matrices of rank n necessarily has rank n (b) the set of such matrices of rank 0 necessarily has only one element (c) the sum of two such matrices of rank 1 necessarily has rank 1 Select one: O None of the others apply O (a) yes (b) no (c) no O (a) no (b) yes (c) yes O (a) yes (b) yes (c) no O (a) yes (b) depends in the field, which was not specified (c) no

Q: 8.Find the inverse of the given matrix -3 7 4 -7 3 -6] 1 A = -1 -1 -3 A) A¹ = 0 0 1 B)A-¹ = C) A-¹ =…

A: I have given the answer in the next step. Hope you understand that

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: Prove the following 1. If A and B arenxn matrices over field IF. Prove that trace (AB) = trace (BA).…

A: We have to Prove the following1. If A and B are n × n matrices over field F. Prove that trace (AB) =…

Q: Given that P and O are 3 x 3 invertible matrices then (A-"B) = A. AB-! B. B-'A C. B-'A-! D. BA-

A: Given : A-1B-1

Q: 4. Find the null space and column space of the matrices 0 1 1 -2 1 1 0 1 22-4 0 -1 0 1 -3 A = 1 2 3…

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Q: (i) Use the definition of inverse to prove the following: if A and B are n × n nonsingular matrices,…

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A: Determinant properties help to find the determinant of the given matrix. Determinant property for…

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A: Given two matrices are , (A) 1-5000  0100  001     ,  (B) 0101-14001    (.) Row reduced echelon form…

Q: A square matrix U = [ui] is said to be upper triangular whenever Wij = 0 for i>j-i.e., all entries…

A: Note: As you asked answer of subparts (a) and (c) so i answered here only that.

Q: 6. Let A, B, and A+B all be square invertible matrices of the same size. Show -1 that (A+B) = A(A+B)…

A: We need the property (CD)-1 =D-1 C-1  For any two matrices C and D.

Q: 10. True or False: If A, BE M, are nonsingular matrices, then A-+ B- is nonsingular. (a) True (b)…

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Q: 6. Find the inverses of the following matrices using Gauss-Jordan reduction: (41 2 0 -3 3 0 <-4 (a)…

A: Here we have to evaluate the inverse of the matrix a) and b) using gauss jordan method.

Q: 2. Consider the matrices: 1 [1 3 B = 0 0 2 A = -1 5 Setha - Compute the following: (a)(AC – 2B")ʻ,…

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Q: Seven thieves try to share a hoard of gold bars equally between themselves. Unfortunately, six bars…

A: Seven thieves try to share a hoard of gold bars equally between themselves.Unfortunately, six bars…

Q: Consider the following two matrices 1 -5 0. 1 (A)| 0 1 (B)| 1 -1 4 1 Select one: a. (A) is in RREF…

A: We have find the correct option from the given options.

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Q: Q22. If Q, and Q, are n by n orthogonal matrices, then (a) QQ, is also an orthogonal matrix (b) Q-Q,…

A: According to question given that Q1 and Q2 is are n by n orthogonal…

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A: Given that x=(1,1) and y=(5,-1)

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A:

Q: 5. Which (if any) of these matrices are negative semi-definite? -4 0. i.

A: Determine whether the matrix is negative semi definite or not

Q: .3.5. For n×n matrices A and B, explain why each of the following in- equalities is valid. (a) trace…

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Q: 4. If A and B are n x n invertible matrices and c ER, prove or disprove the following statements.…

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Q: Mrs. Wigen conducted a survey in her math class. She asked each of her students to tell her how many…

A: The data plotting helps to visualize the relationship between variables. A dot plot consists data,…

Q: If A is an  m × n matrix with entries in the field F, then                   row rank (A) = column…

A:

Q: Let M₂ (R) be the set of 2 x 2 matrices with real number entries, i.e., b M₂ (R) = { [ a &] |…

A: The given matrix is M2ℝ=abcd: a,b,c,d∈ℝ To find : (a) M2ℝ is a ring under addition and…

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A:

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Q: [1 2 3 5 6? Which of the following matrices are submatrices of A = 4 7 8. [; } 1 2 (c) 8 1 (a) 3 4…

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Q: 4. Show whether that the following matrices are positive define, negative definite or neither A= 2.…

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Q: If A and B are 3 × 3 matrices and detA=2 and det B = 4, find det (5A* BTΑ-)

A: See the details solution in below

Q: 1. Let A and B are two nxn matrices, and I is a nxn identity matrix. If I + AB has an inverse,…

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Q: 4. Prove: If A and B are both n x n matrices, then det(AB)= detAdetB. (Only use 2x2 matrices)

A: Given A and B  n×n  matrices to prove  det(AB)=det A det B

Q: For all square matrices A and B, it is true that det(A + B) = det(A) + det(B) O True O False

A:

Q: Are the following matrices invertible? Choose Choose Choose Choose 1. ✓2. < 3. 4. 4 3 -9 -4] 45 20…

A: