Answer if it\'s true or false for each. 24. True False 25 True False 26. True Fa

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Answer if it's true or false for each.

24. True False 25 True False 26. True False 27 True False 28. True False 29 True False 30. True False If A is non-singular, then det(ATA) is positive. For 2x2 A, if det (A) 0, then A has two distinct real eigenvalues. There are nxn matrices A, B, C such that AB C, where A is singular, B and Care non-singular. The eigenvalues of a square matrix are the entries along the diagonal If A1, M2 are complex conjugates, then so are their associated eigenvectors. For mxn A, if you know what Av1,Av2 Avn are, where vn is a basis for R then you know Av for every vector v in Rn, and can figure out what A is. H (t) f(t) f(t), where H(t) is the Heaviside unit step function

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24) The statement is TRUE

A^TA = ||A||^2

Since the mod function can never be negative and it is given that A is non-singular, hence det(A) is not zero, therefore the modulus of ||A||^2 will always be greater than zero

25)

The statement is FALSE. since the eigen values can also be imaginary

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