2 0 -9 3 0.9 1 15 Given Matrix A = a) What are the dimensions (the size) of matrix A? b) What element is represented by a12 (also shown as a1.2 sometimes)?

Q: [5 Consider matrices A =9 -11 11 and B =|0 -1] Two elementary matrices -4 c) 2. 8. 4 1 -1 3 -4 2. E…

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Q: 1 4 3 2 1 0 3 1 1 2 1 4 5 32 0 1 2 0 1 Consider the block matrix A = What are the dimensions of A21?…

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Q: 30: If reflection about origin is represented by the matrix R reflect the letter %3D ro 4 4 1 1 01…

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Q: 4 1 8. Find a value of a such that the matrix A is non- %3D diagonable; explain the reason and then,…

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Q: 1. to the identity matrix I using elementary row operations. 12 (a) Reduce A - 1. as a product A =…

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Q: Г1 8 5° Let B = 0 9 5. Find a triangular matrix A with positive diagonal entries such that A2 = B.…

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Q: Consider 12 1 2 13 -1-3 4 Convert A to an upper triangular matrix U by using Gaussian elimination…

A: The given matrix, A=121213-1-34 The upper triangular matrix is of the form A=a00bc0def To find a…

Q: Determine the dimensions of Nul A, Col A, and Row A for the given matrix. 15 3 3 0 7 6 0 15 -4 0 3 3…

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Q: 1 -1 10 Let A = Construct a 4 x2 matrix D, using only 1 and 0 as entries, such that AD = I,. Is it…

A: Here, it is given that A=1-110-1101 We need to construct a matrix having entries 0 and 1 only such…

Q: 3 91 Given a matrix A3 9 6 7] which of the elements aij follows the condition i=j. 9,9,1

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Q: The dimensions of the following matrix is: r2 6 11 4 7 8 1 0 6 7 4 862 1.

A: Clearly there are 5 rows and 3 columns.

Q: 1 5 Let A = then the Cayley-Hamilton Theorem for matrix A is ... -8 2 A2-3A+42| =0 A2- 2A +40 I = 0…

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Q: 11 A square matrix A is orthogonal if AA" = 1. What properties must be possessed by the columns of…

A: Given:

Q: 1.6.1(b,c) Is given matrix diagonalizable? If so, what are the corresponding matrices P and D? 1 1 0…

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

Q: 1 4 Let A= and let B be an unknown 2×2 matrix. Calculate det B given that 1 2 det(AB)= 32.

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Q: 4. Given the matrix C = 463 9 -2 5 5 1 12 48 -3 find bases for both the row space and column space…

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Q: 5. Suppose that A is a 5x5 matrix with real entries and det(A)=7. a. What is the det(2A)? b. What is…

A: For any n×n matrix, it can be written that det(kB)=kndet(B) . For two matrices, A and B, it can be…

Q: A matrix A is similar to matrix B, if f invertible matrix P, B = P'AP. Prove is similar to B and B…

A: Given that: A is similar to B such that: B=P-1.AP.

Q: 4 - 6 8 - 2 - 8 and C = 3 Verify that AB =AC and yet B# C. 3 Let A = B = 7 - 8 12 Show the…

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Q: 1. 2 3 Question 3. Consider the matrix A = 2 3 4 Is there an orthogonal matrix P and a diagonal…

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Q: 2. Decompose the given matrix as indicated: [25 5 4] 10 8 16 8 12 22 1 Answer:

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Q: 2 3. 1] Given that matrix P =0 2. Find the matrix A such that A = PBP 1, where 1] -1 1 -2 0 01 B is…

A: Given:The matrix P=2310-12101 , B=-200030006To find:we have to find the matrix A such…

Q: 1) The dimension of the matrix 3 -2 1 0 4 2 1 2 a) O 2 x 2 b) O 4 x 4 c) O 4 x 2 d) O 2 x 4 is

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Q: 1. Suppose that A is a 6 by 10 matrix with rank equal to 4. (a) What are the possible number of…

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Q: 1 4 If L= ,U = are factorization of a square matrix A, where L is lower triangular matrix and U is…

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Q: -10 1 Let A = Construct a 4 x2 matrix D, using only 1 and 0 as entries, such that AD = I,. Is it…

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Q: [1 23 A 3 4 5] Given matrix A above, in the matrix multiplication: IxA = A.What is matrix To create…

A: Find your answer below

Q: 1. Find a matrix K such that AKB = C, given that: 1 4 8 -61 -1 6. [2 0 ; B = 6 -2] A = -2 3 ; C: 6 1…

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Q: 2. Given the matrix A below, Solve for IAI-¹ A = 1 2 2 1 -1 3 4 6 3 5 2 -3 -3 8 7 4.

A: We have , A = 123424681357-12-34 We need to find , A-1 To find the inverse of matrix , augment it…

Q: 1 1 1 A =1 1 1 1 2 1 . How many nonzero elements are there in the adjoint matrix of matrix A?

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Q: 9. 7 Find the rank of the matrix A = 1 -2 %3D 27 21 13 rank(A) = %3D

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Q: [1 8 5] 0 9 5 Let B = Find a triangular matrix A with positive diagonal entries such that A² = B. 4

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Q: 3. Consider the following matrix: -31 A = |-3 -4 -1 -2 3 2 9. (a) Verify that A is diagonalizable.…

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Q: [1 Find a matrix A = -4 -51 = l3. y] 1 z such that A² 10 %3D Lo 1. Lo

A: Given A=1xy01z001 A2-0-4-50010000=I3 To find Matrix A:

Q: 14 3 Which of the followings are TRUE about matrix A =0 6 4? 0 0 1 I Matrix A is a lower triangular…

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Q: (1) Find A = LU, where L is a unit lower trian- gular matrix and U is an upper triangular matrix (by…

A: Given: A=2101-2-22-121336115 and b=0006. To find: LU decomposition of given matrix and hence solve…

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…

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Q: 1) Consider the following matrix: 1 7 8 8 A = 1 3 3 -2 -5 1 -8 Answer the following questions: 1.1)…

A: R is row echelon form not row reduced echelon form.

Q: 3 3 , Let M 1 -2 -3 Find c1, C2, and C3 such that M3 +¢¸M² + c2M + C3I3 = 0, where Iz is the…

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Q: 8 -6 Find the matrix P that diagonalizes A and the resulting diagonal matrix D. -2 4 4 3 1 D= P =…

A: The solution is given as follows :

Q: (1) If E is an m × m elementary matrix and A is an m x n matrix, then the column space of EA is the…

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Q: Determine the dimension 31 43 -8 21 Ab X of the matrix. AN

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Q: 10. Suppose A is the n x n zero matrix (where all entries of A are zero), describe the solution set…

A: We have to find the solution set of system.

Q: 10. Find a diagonal matrix A that satisfies the given condition a) b) [9 0 0 A- = |0 4 0 A = |0 -1

A: Diagonal matrix are the matrix whose all entries except the diagonal entries are zero. Diagonal…

Q: 1 1 1' Let A be a 3x3 diagonalizable matrix, P 1 1 p-1- 0 1 2. 0 0 -2 D 0. If P-'AP = D then A2 is…

A: I have explained all necessary information in the solution part

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 ?…

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Q: 5 3 Let A=2 -1 8 -7 4 3. 2-1 33 8. Find an elementary matrix E that satisfies the equation EC = A…

A: The Given Equation  is :  EC=A⇒ECC-1=AC-1⇒E=AC-1---(1) Now we will find C-1…

Q: a) Prove that the matrix A = is diagonalizable if –4bc (a– d)². What happens when –4bc = (a– d)² ?

A: Given,         A= abcd

Q: 8 6. Let A -4 -2 Find two different diagonal matrices D and the corresponding matrix S such that A…

A: Given:    2x2 Matrix is given