5. Ineach part, determine whether the matrices are linearly inde- pendent or dependent. in M2 a. [1 b. [o o [o 0 in M3 1

Q: Find the elementary matrix E such that EB = A where %3D 2 3 1 2 3 1 A = 4 -3 -2 and B = -8 6 4 7 -6…

A:

Q: Find the elementary matrix E such that EB = A where %3D 5 4 1 ] 4 1 A = |4 |7 -6 1 -1 and B = |12 3…

A: EB=A multiplying with B-1 on both sidesEBB-1=AB-1E=AB-1

Q: find an oxohogonal or unitary dragonalizing or matrix cach The to lloweng bor 2 (a) (b) 3 -i 4 o 0 2

A: Solve the above question.

Q: (16) Which of the following is a symmetric matrix? (Select all correct answers) ro 1 21 O1 0 1 l2 0…

A:

Q: e) Let A be an n x n matrix. If det(A – AIn) = 0 for some ) e R, then det(A² – X²In) 70.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: Consider the Az 1 34 17 9 203 2 8 16 6 0 5 /

A: (a) We know that we can find the determinant of the matrix by expanding along any column or row.…

Q: ^T) + (B^T) and (AB)^T = (A^T)(B^T) if the orders of matrices are appropriate. * False

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Q: Find the elementary matrix E such that EB = A where 4 1 4 4 1 3 -1 -2 and B 18 -6 -12 %3D 5 -7 4 -7…

A:

Q: 5. Let A be an n x n matrix. Show that if B = S-¹AS for some nonsingular matrix S, then det(B) =…

A: Here, given that: B=S-1AS

Q: D If A is a square matrix and B= A". (A - A"). A show that matrix B is an inverse symmetric matrix.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 8. Prove that (i) ||7. =1, and (ii) |. =\n (I is the Identity Matrix of order n).

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Q: Which matrix in the follows is in echelon form ? 1 2 01 [1 0 1 0 [2 0 2 01 0. A= 00 1 2 0. 1 0 0 0 1…

A:

Q: 6. For any two nx n non-singular matrices A and B, then (a) K(A. B) ≥ K(A). K(B) (c) K(A. B) K(A).…

A:

Q: Let A = diagonalizable matrix( A = XDX-1), then X and D are: LO H O4

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Q: 16. If A is a non-singular matrix such that A - A - 1 = 0, then A1 =? A. A В.А-1 C. A+1 D. 1-A

A: “Since you have asked multiple Questions, we will solve the first question for you. If you want any…

Q: 7. The rank of an identity matrix of order n is: А. п - 1 В. п C. n+1 D. 0

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Q: If A is n x n matrix and (I- A)² = I- A then O a. AT = A %3D O b. AT A = I O c. AAT = I Od. A? = A

A: We have to solve given problem:

Q: Let A =mnd B- then the matrix (2AB + A")" is equal to O None of these O equal to the above 2 17

A:

Q: Let A and B be two matrices of size 4 x 4 such that det(A) = 3. If B is a singular matrix then…

A: Let A and B be two matrices of size 4 x 4

Q: 1 4 What is a, if A = is a singular matrix ? %3D 2 a

A:

Q: IF A is a nonzero n X n matrix such that A = 0, then A is singular. Select one: O True False

A:

Q: 7. Suppose U is an m x n matrix and V is an n x m matrix for which In-VU is invertible. Show that…

A:

Q: 13. a) Show that if A and B are n x n matrices, at least one of which is invertible, then AB and BA…

A: (a) If A and B are two n×n matrices, and one of them is invertible, then show that AB and BA are…

Q: If A and B are 3×3 invertible matrices, such that det(A)=2, det(B) =-2. Then det (ABA^T) = ???

A: To solve this problem, we use the standard result of matrix

Q: 20. The following are rules of transposition of a matrix except: (explain) a. (A")" = A b. (A + B)"…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Let A be a nonsingular matrix. If det(A)=3, then det(A) = %3D

A: In this question we have to find detA-1.

Q: Which of the following is an elementary matrix? 1 0 1 В. 1 C. 0 0 1 A. 5 1

A: Given : Matrices A.  10-51 B. -5110 C. 110001000 D. 2002010000100001   To find : Which of the…

Q: 1) Suppose that T is a linear operator with standard matrix 8 3 6 0 2 0 0 7 Is T one-to-one?…

A: Given the linear operator T:ℝ3→ℝ3 836025007 Now, we find determent of T.…

Q: •(b) A = B:

A: Given,        A=-1201,   B=1-201

Q: 3. If A is a nonsingular matrix, then A' is nonsingular and its inverse is (A')1 = (A') '. Prove it!

A: A matrix A is said to be invertible if and only if  det(A) is not equal to zero i.e.  |A| ≠ 0

Q: 1. Suppose (B – C) D = 0, where B and C are m x n matrix and D is invertible. Show B = C

A: ( B - C )D = 0 where B and C are m × n matrix and D is invertible.  Then, we have to prove that B =…

Q: Let A = 0 1] 3 03 0 0 2 = If possible, construct P and D such that A don't need to compute P-¹).…

A:

Q: (g) Suppose A and B are real normal matrices satisfying AB* = B*A. Show that A+ B and AB are both…

A:

Q: Let A and B be two matrices of size 3 x 3 such that det(A) = -2 and det(B) = 3. Then det(2A-1B") =…

A:

Q: Find the elementary matrix E such that EC = A where 3 3 -3 1 3 3 1 A = -1 and C = 2 -3 | 8 -7 2 23…

A:

Q: 16. Prove that for any square matrix A, ||A||ž E ||A* A||2.

A: Given: A is a square matrix.

Q: The following augmented matrices represent different linear systems In x, y, z Which of the linear…

A: The augmented matrices are given then which linear system has unique solution.

Q: (8) Let A and B be m x n matrices. Prove that the rank of A + B is less than or equal to the rank of…

A:

Q: 6. Show that (AA)* = X* A* for all A E C and all matrices A.

A:

Q: Is it true or false? If A and B nxn matrices |A+B|=| A |+ | B| Birini seçin: O Doğru O Yanlış

A: we have to identify the following is true or false

Q: Let A and B be 0 1 -3 1 2 A = 1 2 B = 0 1 -3 2 2 -1 2 2 -1 | Find an elementary matrix E such that…

A: When we perform a single row operation on this identity matrix we get a matrix known as the…

Q: Find the elementary matrix E such that EC = A where %3D 4 4 A = |3 -1 and C = 3 0. -1 9 -8 19 0 4 ?…

A:

Q: 4. Suppose that a, b, c, d, x, y, z are real numbers, and consider the matrix 0 0 0 d 0 0 c 0 b y 0…

A:

Q: 6. For any two nx n non-singular matrices A and B, then (a) K(A. B) ≥ K(A). K(B) (c) K(A. B) K(A).…

A:

Q: 21 1 2 1 ol -1 A = | 0 2.

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Q: -2 a wi a 8 Consider the matrix A = Oa. a = 4 O b. a = -4 OCAERI{- 4,4} Od. A is invertible for any…

A: Given:A=-2 aa8 Where  a∈ℝA is non-invertible matrixNon -invertible:     If the determinant of the…

Q: If A is an invertible matrix and det(A) = 7, what is det (A-1)?

A: Given: If A is an invertible matrix and det(A) = 7 To find: what is det (A-1 )?

Q: [*:* а + 2 а (10) Find all a E R for which the matrix is singular. 1 а

A: Remark: A square matrix A of n is said to be singular if and only if det(A) = 0. i.e., Its…