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 Matrix 20 Flashcards |
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The trace of a square matrix is defined as ___ of the elements on the main diagonal. |
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The sum |
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True or False: A symmetric matrix satisfies the condition aij = aji for all i and j. |
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True |
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If A is a square matrix and A is singular, then | adj A | = ___. |
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0 |
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True or False: The adjoint of a diagonal matrix is also a diagonal matrix. |
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True |
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What is the relationship between the determinant of a matrix A and its adjoint? |
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| adj A | = | A |ⁿ⁻¹ |
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If A is an idempotent matrix, then ___ = A. |
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A² |
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What is the transpose of a matrix? |
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The transpose of A, denoted AT, is obtained by interchanging rows and columns of A. |
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True or False: The transpose of a product of matrices follows the rule (AB)T = BTAT. |
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True |
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If A is a matrix of order 3 x 2, what is the order of its transpose? |
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2 x 3 |
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If an n x n matrix A has a trace of 10 and another matrix B has a trace of 5, what is the trace of A + B? |
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15 |
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