Quèstion 6 T(x, y, z) = (3x-4y, 5y+z), then the standard matrix of T is O[3 5 4 -1 3 4 5 -1 None 34 0 !0 5 -1

Q: Question 20 Given that A= 12 -5 has the form A= PCP-¹, C- 0c-12²2 C OP-11 0 -3 -1 and P = Op- and P…

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Q: Question 3 Let 1 -2 22 -11 1 1 A =0 -1 and P = 0 1 0 -1 1 0 0 P diagonalizes A , then compute the…

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Q: If A and B are two n x n invertible matrices, then one of the following is always correct a) (AB)T =…

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Q: Question 2. Is the matrix P orthogonal, where P- (; ) 1 YES NO 1 V3/2 0 1/2 P = -1 YES NO V3/2, 1 -

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Q: Question 28) Determine whether the given matrix is elementary. (a) (b) (c) (d) 외 1 0 -5 1 -5 1 10 1…

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Q: Question 8 Which ONE of the following matrices is NOT diagonalizable? 1 0 0 050 0 0 5 4 -2 0 5 0 6 1…

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Q: Question 5: Let 1 A = 1 15 -2 (5a) Find a 3 × 3 matrix P and a diagonal matrix 0 A2 0 13 D = || such…

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Q: Question 3. Let 1 0 1 0 0 0 2 1 A = 1 Find an orthogonal matrix P such that P-'AP is diagonal.

A: Given: A=110110002To find an Eigen values:The Characteristic…

Q: QUESTION 12 Find a matrix P such that 1 0 23 0 3 1 -1 O A. P 0 1 1 1 O B. P = 1 0 O C.P 1 0 OD.P -1…

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

Q: Question 1 Let 1 1 -1 A = -1 6 Find det(A) by reducing A into a triangular matrix.

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

Q: Question 3. Let 1 1 1 0 0 0 2 A = 1 Find an orthogonal matrix P such that P¯'AP is diagonal.

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Q: Question 2 Consider the matrices 3 A = and 6. x - 4 -9 Find the possible value(s) B = x + 4 of x…

A: As per the company's guidelines we are supposed to solve first question for you, kindly repost other…

Q: Question #9: A square matrix for which all diagonal elements are equal to 1 and all nondiagonal…

A: As per our guidelines we are supposed to answer only first question ( if there is no specific…

Q: Question 5 Find an invertible matrix P and a diagonal matrix D such that PAP=D. 0 2 A = 12 10 18 3…

A: Let us find out A-λI = 0

Q: Question 14 Let B = {b1, b2} and C = {C1, c2} be two bases for R, where [1 41 2 [1] C2 = 8 b1 3 b2 >…

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Q: Question 3 Consider the matrix 1 1 3 A = 1 2 4 1 4 Use Cramer's rule to find, if possible, the…

A: We use cramers rule

Q: Question 1 Let A and A' be two matrices defined below (0 1 1 1 00 0 0 0 0V 100 0 1 10 0 0 0 100 0 00…

A: Since the questions contains many subparts as per the guidelines I am answering the first three…

Q: Question 3. Let 1 1 0 A = 1 1 0 0 2 Find an orthogonal matrix P such that P-1AP is diagonal.

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Q: Problem 2. For any matrix A € M„(F), show that (Ar, y) = (x, A*y) for all a, y E F". Use this to…

A: Please check the answer in next step

Q: Question 18 Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a…

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Q: Question 11 Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix…

A: Introduction: Due to the ease with which diagonal matrices may be handled—their eigenvalues and…

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: Question 7 a) Provide the definition of diagonalizable matrices. (;:) 1 2 b) Use matrix A = to…

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Q: QUESTION 8 Which of the following matrices are in echelon form? O1 23 4 001 2 01O1 O[1011 0 0 0 0…

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Q: Question 2. Is the matrix U unitary, where 1+ i 1- i -1 Yes No 1- i | 1+i P = diag ( i,-i, V2 Yes No

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Q: Question 13 Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix…

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Q: Question 2: (a) Show that for 2 × 2 matrices A &B the following equation holds. det(A + B)? = [det(A…

A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the next…

Q: A =

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Q: Problem 7. Let A be an nxn matrix. (a) Prove that if A is singular, then adi A must also be…

A: # as per the guidelines we are entitled to solve one question at a time ,please resubmit the other…

Q: Question 41 Consider a symmetric matrix A = '). when is A positive definite? When a > 0 and det(A) >…

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Q: (: :). Question 1. Are matrices e M2,2: 2 2 a basis of M2,2? YES - NO

A: We need to answer if the matrices (1111), (1222)∈M2,2 are a basis of M2,2 (YES-NO)

Q: Question 44 Select the matrix corresponding to the quadratic form Q (21, 12, 13, 24) = -2xf + 5x –…

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Q: Question No.4: Find the proper assignment of the following matrix. JI Employees/Jobs El J2 J3 11 14…

A: ASSIGNMENT PROBLEM

Q: Question 7 Consider the matrix 5 1 1 4 2 1 2 1 A= 4 (a) or Positive definite? (Justify your…

A: We have to solve given problem:

Q: Question 3 2 3 1 1 Find the (1,1)-entry of matrix X given 1 Let A and B 3 that AX+A=B. 4 1 2

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Q: Question 14 Let B = {b1, b2} and C = {c1, c2} be two bases for R, where [1 2. b1 b2 3 > C1 13 C2 =…

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Q: Question 5 Find an invertible matrix P and a diagonal matrix D such that PAP=D. To -2 1 A = 2 -4 1 4…

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Q: Question 2 Suppose T:R° → Rª is defined by T(x) Mx and M is a 4 x 13 matrix. Then a = 6 =

A: For the given statement

Q: Problem 6. Let A be an mxn matrix. Show that if AA" = Omxm, then A = Omxn:

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Q: Question 18 If A and B are n x n matrices and rank( A) = rank( B) = n, then O A. rank(AB) = 2n OB.…

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Q: Question 6 The matrix A is the standard matrix for the trans 4² -2 24 4 8 -12 -3 5 01 31 O2 31 ° 27…

A: Given, matrix A is standard matrix for the transformation x→Ax. It transformed 13 in 11 and 27 in…

Q: Question 1 5) Consider the matrices 4 1 1 A =| -6 4 10 |. Use Cramer's rule to find, if 1 5 2…

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Q: Question #3 * Two matrices A = [a] and B = [b,] are equal if and only if A and B are of the same…

A: As per our guidelines we are supposed to answer only first question ( if there is no specific…

Q: 1 2 2 2 e M2,2: Question 1. Are matrices a) Linearly independent?

A: We will check whether the given matrices are linearly independent or not.

Q: If A is a 2 x 2 matrix such that det (A) = -3 then det(5A) equals Select one: O - 75 O 15 O None of…

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Q: Question 4 Consider the matrix A = 10 3 1 0 Express A in the form A = EFGHR, where E, F, G and H are…

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Q: QUESTION 2 Which of the following matrices is not an elementary matrix? 1 (D) 0 1 0. (A) (B) (C) 2 0…

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Q: Question No. II Show that the column vectors of following matrix A are linearly independent: [1 0 07…

A: GivenA=100621432To showColumns of A are linearly independent.

Q: QUESTION 22 The matrix A below is orthogonal. 2 3 2 A = 3 3 2 4 5 3 3 3 O True False N/3 1/3

A: 22. A real square matrix is said to be Orthogonal when the product of a square matrix and it's…