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Use the Laws of Logarithms to combine the expression. 3 log4 A + 5 l.pdf
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### True or False If False, explain why. 6. For any invertible matrix A,.pdf

1. True or False? If False, explain why. 6. For any invertible matrix A, the matrix (AA^T) is positive definite. 7. If A is an orthogonal matrix, then det A= 1. 8. Two matrices are similar if and only if they have the same characteristic polynomials. 9. Any finite dimensional inner product space has an orthonormal basis. Solution 6) we know that : A real symmetric matrix 'M' is positive definite iff there exists a real nonsingular matrix 'A'such that M=AAT so (6) is true. 7) AAT=I => |AAt|=|A|2=1 => |A|= 1 or -1 so false 8) Similar matrices represent the same linear transformation so TRUE 9) TRUE : it follows matrix theorem refer http://cims.nyu.edu/~kiryl/Algebra/Section_4.4--Inner_Product_Spaces.pdf (theorem 4.4.2) 10) FALSE, innet product is defined by XTY only
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