only a,b,c,d 4. Which of the following set-operation pairs are groups? All matrices are with real entries.Please prove each answer but feel free to cite any facts from linear algebra.(a) n x n matrices with matrix addition.(b) n x n matrices with matrix multiplication.(c) n x n diagonal matrices with matrix multiplication.(d) n x n diagonal matrices with no zero-entries in the diagonal, with matrix multipli-cation.(e) n x n matrices with non-zero determinant (this is called GLn (R)), with matrixmultiplication.(f) n x n matrices with determinant +1, with matrix multiplication.(g) n x n orthogonal matrices (an orthogonal matrix is a matrix whose columns areortho-normal to each other, equivalently AT A = I), with matrix multiplication.

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4. Which of the following set-operation pairs are groups? All matrices are with real entries. Please prove each answer but feel free to cite any facts from linear algebra. (a) n x n matrices with matrix addition. (b) n x n matrices with matrix multiplication. (c) n x n diagonal matrices with matrix multiplication.

4. Which of the following set-operation pairs are groups? All matrices are with real entries. Please prove each answer but feel free to cite any facts from linear algebra. (a) n x n matrices with matrix addition. (b) n x n matrices with matrix multiplication. (c) n x n diagonal matrices with matrix multiplication.

Advanced Engineering Mathematics

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ISBN:9780470458365

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Chapter2: Second-order Linear Odes

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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only a,b,c,d

4. Which of the following set-operation pairs are groups? All matrices are with real entries.
Please prove each answer but feel free to cite any facts from linear algebra.
(a) n x n matrices with matrix addition.
(b) n x n matrices with matrix multiplication.
(c) n x n diagonal matrices with matrix multiplication.
(d) n x n diagonal matrices with no zero-entries in the diagonal, with matrix multipli-
cation.
(e) n x n matrices with non-zero determinant (this is called GLn (R)), with matrix
multiplication.
(f) n x n matrices with determinant +1, with matrix multiplication.
(g) n x n orthogonal matrices (an orthogonal matrix is a matrix whose columns are
ortho-normal to each other, equivalently AT A = I), with matrix multiplication.

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