Proof that if matrix A is diagonalizable, then AT is diagonalizable.

Q: a) Is A diagonalizable? Explain. b) If A is diagonalizable, rewrite A as XDX-1 (explain the choice…

A: a) Given            A=310010-310

Q: Prove that diagonal matrices are symmetric matrices.

A: Given: diagonal matrices are symmetric matrices

Q: upper triangular matrix is upper triangular (Use matrix transposition)

A: Here ,we have to prove that the inverse of an upper triangular matrix is upper triangular.

Q: Prove Any n by n triangular matrix with main diagonal entriesare all 1 is diagonalizable if and only…

A: Triangular Matrix: A triangular matrix is a square matrix where all the values above or below the…

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

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Q: snip

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Q: Prove (include a hypothesis and a conclusion), that if A, B, and A+B are invertible matrices, then…

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Q: Let A be a 3 x 3 symmetric matrix given by A = 2 -1 0 -1 0 2 -1 2 -1 Find an upper triangular matrix…

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Q: (Linear Algebra) Let M be a rectangular matrix with linearly independent columns. Prove that M^T * M…

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Q: Prove that every symmetric upper (or lower) triangular matrix is diagonal.

A: Solution: Consider the given statement " Every symmetric upper (lower) triangular matrix is…

Q: hat is the kernel matrix? the statement that any diagonal matrix is a valid kernel matrix is true?…

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Q: Is a singular matrix consistent/inconsistent? Is a nonsingular matrix consistent/inconsistent?

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Q: A" A is invertible if and only if A has linearly independent columns.

A: ATA is invertible if and only if A has linearly independent columns.

Q: The matrix 4-[²₁2] A = -1 Determine whether A is diagonalizable. If it is, identify an invertible…

A: Matrix is said to be diagonalizable if it had distinct eigen values.

Q: This question examines your understanding of linear mappings and their relation with matrices.…

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Q: Suppose A is invertible.  Explain AT A is invertible.

A: The transpose of an invertible matrix is also invertible, and its inverse is the transpose of the…

Q: Every skew-hermitian matrix (i.e. A" = –A) is normal. True False Every unitarily diagonalizable…

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Q: 5. Is the matrix ㅇ 15 아가 Unitary? Explain. 블 ܐ ܥܙܐܡ ܝܐܐ ܙܐ3 춤을

A: A matrix is the arrangement of elements in a row and columns into a rectangular array. The order of…

Q: Find the singular values of the matrices in Exercises

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Q: Prove that if the diagonal entries of a diagonal matrix are permuted, then the resulting diagonal…

A: Permuting the diagonal entries of a diagonal matrix D amounts to permuting the rows of that matrix…

Q: Prove that for a diagonal matrix, the 1-,2-,∞- and -norms are the same.

A: We are given a diagonal matrix D. We wish to show that D1=D2=D∞ If we write D=d10⋯00d2⋱⋮⋮⋱⋱00⋯dn…

Q: Orthogonally diagonalizable the following matrix 2 1 1 C = -1 1 1 0 -1 1.

A: The solution is below.

Q: If b1, b2 , b3 is a basis of IR and A, B are 4 × 3 matrices satisfying Ab; = Bb; for i = 1, 2, 3…

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Q: Prove [A, B] not positive and A,B are square matrices(matrix theory) [A, B] = AB - BA.

A: Given: It is given that A,B=AB-BA where, A and B are square matrices. To prove: We have to prove…

Q: (a) Hermitian, skew-hermitian, unitary and diagonal matrices are all nor- mal.

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Q: find an example of a matrix in V=M3x3 that doesn't have an additive inverse ans should be entries in…

A: We have to give an example of matrix in V=M3×3 that does not have an additive inverse.