Let the charasteristic polynomial of a 3 x 3 matrix A be p(2) = 13- 1. Suppose that A2002 = aA? + bA + cl where I is the 3 x 3 identity matrix. What are the values of a, b and c? a-) a = 0, b = 0, c = 1 b-) a = 0, b = 1, c = 0 c-) a = 1, b = 0, c = 0 d-) a = 0, b = 1, c = 1 e-) a = 1, b = 1, c = 0

Q: Let Q be an orthogonal matrix such that QA makes sense. Show that A and QA have the same singular…

A: Let,

Q: Let C be an nxn matrix that satisfies C2 -3C–2In 0. Show that C is invertible and C=1 = }(31-A)

A:

Q: Let A be any m×n matrix, Omn be the m×n zero matrix, and c be scalar. Show that if cA = Omn then…

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Q: Consider the 6 × 8 matrix 3 0 0 0 0 1 2 1 0 0 0 0 1 0 0 -3 4 -7 -9 A = 0 0 0 0 0 0 0 0 0 1 8 1 and…

A: The main objective is to answer the sub parts by using given matrix which is in reduced row echelon…

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A: We want to prove that AB and BA are square matrices

Q: Find a (2x2) singular matrix A that maps (2, 4) into (3, 1).

A: Singular matrix mean its Determinant is equal to 'zero' .

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A:

Q: z= 5x, + 12x2 + 4 x, S.t X, + 2x2 + X, s 8 2 x, - X2 + Xạ = 8 where x,, X2, Xs 20

A: For a Minimization Problem, The constraints must be in the form≥ in the standard Primal Form.…

Q: Let A be a 3 x 3 matrix such that A3 - 6A² + 4A – 31, = 0. Then, A is invertible and A

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Q: Let A and B be nxn inversible matrix. Prove that AB is invertible and (AB)-1=  B-1A-1.

A: Let A and B be n x n invertible matrices, with inverses A-1 and B-1, respectively.

Q: Prove that any square matrix A can be written as the sum of a symmetric matrix and a skew­symmetric…

A: To Prove Any Square matrix A can be written as the sum of a symmetric matrix and a skew­symmetric…

Q: Give an example of a 2 x 2 matrix A such that im(A) =ker(A). %3D

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Q: If A is a real n xn matrix, show that AA" and ATA are similar. (Hint. Start with an SVD for A.)

A:

Q: Let A be a symmetric positive definite n×n matrix. Show that A can be factored into a product QQT ,…

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Q: Find x such that the matrix is singular. 4 X A -2-6 X3D

A: Given Matrix is, A=4x-2-6 we know that, A matrix is said to be singular if it's determinant is zero.…

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Q: Find the change of basis matrix from B2 to B1. -4 B1 = , B2 B2 = 2

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A:

Q: Suppose A is a 2 x 2 matrix such that A and 1 A What is A-1?

A:

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A: LU decomposition of the matrix

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A:

Q: * Let A be and m x n matrix. Describe the matrix E such that EA is A with row swapped.

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A: From rank plus nulity theorem we know that : rank A + nullity A = the number of columns of A  From…

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A: We find the sum of squares of the singular values in terms of A.

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Q: Let A be an m × n matrix such that ATA is invertible. Show that the columns of A are linearly…

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Q: Prove det(A) = det(A'), for an upper triangular matrix A.

A:

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A: Given:Let r1.......rp be vectors in ℝnLet Q be an m×n matrix Qr1.......QrpR=r1.......rpQ=Q…

Q: 2. Let the rref of a matrix A be, 0 2 0 -2 0 1 -5 0 -3 0 0 0 1 6 Determine A if the first, second…

A:

Q: Find a (2x2) singular matrix A that maps (2, 2) into (1, 2).

A: Here in this question find a 2×2 matrix that maps (2,2)  into (1,2). Here i attached solution of…

Q: Let A be an m xn matrix. Explain why the matrix ATA is symmetric.

A: A square matrix is symmetric if  A^T = A

Q: Is it true that when an n*n matrix whose columns form a basis of R^n, then A is invertible?

A: We shall answer this in next step

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A: Consider the provided question,

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Q: Show that (-A) T= -A", where A is a 2x3 type matrix (you can show it on the example)

A: Let matrix A=abcdef. Order of matrix A is 2×3. ⇒-A=-a-b-c-d-e-f ⇒(-A)T=-a-d-b-e-c-f  →Result 1

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A: AB and BA are both defined.

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A: First we need to find eigen values:

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A:

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Q: 2. Let the rref of a matrix A be, 1 0 2 0 -2) 0 1 -5 0 -3 0 0 1 6 Determine A if the first, second…

A: