Define what it means for a function Q : R" R to be a quadratic form. Furthermore, explain how we obtain a unique symmetric matrix associated to Q.

Q: Find the spectral decomposition of the matrix 可

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Q: Let A = [aj be a 4 x 4 matrix. Develop the general expression for det(A).

A: Given:               Matrix A is : [aij] is the 4×4 matrix;   General expression for the determinant…

Q: Express the invertible matrix (1 2 1 10 1 1 2) 1 as a product of elementary matrices.

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Q: Use the Invertible Matrix Theorem to decide if A is invertible

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Q: Find the standard matrix for the reflection T of R³ on the line , = . Your work must be shown! Is T…

A: We will first take an arbitrary point (x,y,z) then calculate its reflection point (x',y',z') about…

Q: let Amxn matrix , c scalar If cA=0, then Select one: a. c=0 and A=0 b. c=0 or A=0 C. C0 or A=0

A: WE have to check the meaning of cA=0.

Q: Let the matrix below be Anti-symr

A: Anti symmetric matrix is also known as skew symmetric matrix.

Q: Prove the theorem: AAT is a symmetric matrix for any matric A.

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Q: Show that if A is a symmetric matrix, then Ak , k = 2, 3,... , is symmetric.

A: Given that, A is a symmetric matrix. Then we get, A^T = A; where A^T is the transpose of matrix A We…

Q: Find the matrix C such that BC = AT

A: Let A be an n×n matrix, Then the transpose matrix of A is also an n×n matrix denoted by AT. Now,…

Q: Let A be a 4x6 matrix. what is the dimension of Col A if the nullity is 2? Explain

A: 4

Q: Show that LU decomposition is not possible for the matrix A, where 1 2 3 A 2 4 1 0 2

A: The given matrix is,A=123241-102

Q: Find x such that the matrix is singular. 4-[94] A

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Q: Why is it important that the matrix is invertible? Give and example.

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Q: Let U be an n × n non singular matrix with non zero diagonal entries. Explain why U must be non…

A: Consider the provided question, Let U be an n x n non-singular matrix with non-zero diagonal…

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.…

Q: Let A and B be two square matrices. Assume that both A and B are invertible. Show that BA is…

A: Note that--- If determinant of a matrix is non-zero then the matrix is said to be invertible and if…

Q: Let A be an n × n matrix in which the entries of each row sum to zero. Find ∣A∣.

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Q: Find an example of a singular 2 × 2 matrix satisfying A2 = A.

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Q: How many rows and columns must a matrix A have in order to define a mapping from R* into R³ by the…

A: Find the number of Rows and columns in a matrix A.

Q: Let A be an n × n singular matrix. Then

A: if matrix A is singular that means its determined is zero.so at least one row of matrix A is…

Q: State whether the matrix is diagonalizable or not. 0 0 7 0 O diagonalizable O not diagonalizable

A:

Q: Now assume that f and g are both C2. Express the matrix of second derivatives V²F(x) in terms of f…

A: b)

Q: ind the 3x3 matrix that is equivalent in it's action to each of the

A: Given: To find 3×3 matrix that  equivalent to the symmetry operators are, a  S^2zb  C^2z

Q: Г1 3 2 5 1 [3 4 2

A:

Q: Let B be an invertible matrix. Show that A = BTB is positive definite.

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Q: Find ATA for the matrix. Show that this product is symmetric.

A: The transpose of matrix A is,

Q: verify that the matrices and scalars in Exer- cise 1 satisfy the stated properties. (a) (AT)" = A…

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Q: Use the SVD to show that any square matrix A can be written as A = unitary and P is Hermitian. UP…

A: By SVD, we know that matrix A can be written as A=SDVTWhere S and V are orthogonal matrices andD is…

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

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Q: Let A be a 3 x 3 matrix such that 3a(1)- 2a(2)+7a(3)=0. Is A nonsingular? Explain.

A: A is singular matrix if rank is not full

Q: Compute the standard matrix for the linear map T : R² → R² which (1) rotates i by 0 = T, (2)…

A:

Q: Let A be an x frove that mxh matrix

A: Given A be the m×n matrix. So A* be the transpose of A.

Q: find if the vector x is in the range for matrix A

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Q: -) Let A, B be nx n symmetric matrices such that XTAX = X™BX for all %3D column vectors X e R". Show…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: hat is the matrix for

A: Given, consider the two-tank system shown below. Each of the two tanks contains 200 gallons of water…

Q: Let A be a non-singular matrix, det(A) ± 0. a) Show that µ(A) does not change if the operator A is…

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Q: TRUE/FALSE Assume that all the given matrices are n × n. If A and B are row equivalent matrices,…

A: Given: All the given matrices are n × n. A and B are row equivalent matrices.

Q: Determine whether or not the following matrix is negative (semi)definite or positive (semi)definite:

A: Let A be an n×nmatrix , than 1) A is said positive definite if Di>0 for i = 1, 2, 3, ..., n 2) A…

Q: State whether the matrix is diagonalizable or not. 0 6 0 0 O diagonalizable O not diagonalizable

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Q: Verify that the matrix defines a linear function T that is one-to-one and onto.

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Q: Assume A and B are two m × n matrices with the same reduced echelon form. Show that there exists an…

A: Given A and B are two m×n matrices with the same reduced echelon form. We have to show that there…

Q: Explain why for any matrix A, AA' exists and prove that AA' is a symmetric matrix

A: Let A is any matrix of order m by n Am×n    and   Atn×m Now  AAt exists of order m by m To prove…

Q: State whether the matrix is diagonalizable or not. [:] 0 7 0 0 O diagonalizable O not diagonalizable

A: Given matrix is 0700 and now subtract λ from the diagonal elements=0-λ700-λThe determinant is…

Q: Let A, be the n x n matrix each of whose entries is 1. Show that if n > 1, then In - An is…

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Q: Let Q be an orthogonal matrix such that QA makes sense.                          Show that (QA)+ =…

A: Given, A be a matrix and Q be an orthogonal matrix such that QA makes sense. We have to use product…

Q: Let A be a mxn matrix that n > m (a) Explain why A = 0 has at least a non-trivial solution. %3D

A: (a) Given that A is an m×n matrix. The objective is to explain why Ax=0has non trivial solution.…

Q: - L

A: Given that A=42-12 Take  A-λI=04-λ2-12-λ=0(4-λ)(2-λ)+2=08-6λ+λ2+2=0λ2-6λ+10=0λ=6±36-402λ=6±2i2λ=3±i