# EXAM IN SMN 6190 LINEAR ALGEBRA II

May 29th, 2015
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EXERCISE 1 (20p) -a) Determine by inspection if the given sets are linearly independent or dependent:

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MASTER OF SCIENCE EDUCATION IN NARVIKEXAM IN SMN 6190 LINEAR ALGEBRA IICLASSES: 4 IT, 4 ST, 4 IN, 4 EL, 4 IDDATE: 5. of August 2013DURATION: 4 hoursPERMITTED AIDS: Writing materials which includes a simple calculator and dictionaries THE SET CONSISTS OF 6 TASKS AND HAS 5 PAGES including an appendixREMARK:Selected theory is found at the final part of the setAll answers are to be explainedEXERCISE 1 (20p)a) Determine by inspection if the given sets are linearly independent or dependent: i) , , ii) , , iii) , .b) Decide whether or not the set is a subspace of , when is the set of all matrices of the form . EXERCISE 2 (10p)Given the polynomials , , Show that these polynomials form a basis for consisting of polynomials of degree at most 2.EXERCISE 3 (20p)The vector space consists of all continuous functions on the interval . It is given that defines an inner product on . Let be a subspace of spanned by the functions , .a) Find the value of and conclude what this means.b) Find the best approximation to by functions in . What is the distance from to the plane ?EXERCISE 4 (20p)Find the Singular Value Decomposition (SVD) of the matrix EXERCISE 5 (15p)Find a Jordan form for each of the matrices

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