MAT2310B_04

# MAT2310B_04 - \$&amp;quot;E 9%:— E) Pagelof2 7,52 5% a}: X...

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Unformatted text preview: \$"E 9%:— E) Pagelof2 7,52 5% a}: X j: llﬁltﬂﬁﬁfﬁ‘ \$15MEU The Chinese Universityaof Hong Kong 5-0 03-31 E L0 Oi \$5“; é \$¥ﬂﬁﬁ7¥€iﬁ Course Examination _1_S_t Term, 200i - 2005__ it a ttimz 5% MAT2310A & MAT23 1013 Linear Algebra and Applications Course Code & Tltle : 37+}- Fai IJ‘ Time allowed : ________________ _____________ u hours ________ ______________ __ minutes '55 i £5: if)? E if}; Student ID. No. : Seat No. : _______________________________________________________________ __ Answer ALL questions 1 2 —1 —3 1. Let A = 0 -—1 --2 3 —1 2 3 4 ) a basis for the row space of A, ) a basis for the column space of A, (iii) a basis for the nullspace of A, ) rank 2. (i) Determine Whether xz—x3+5, 2x2—4x—m3, ~5—x2+x3, —x3+32x—7a:2+45, 3m + m2 — 23:3 + 5 span P4 (the vector space of real polynomials of degree less than four). Substantiate your answer. (ii) Find the dimension of the span of cos 23:, cos 3m, sin :3 in C [0.5, 1] (the vector space of real-valued functions deﬁned and continuous on [0.5, Justify your answer carefully. 3. Are the vectors (2, —1,0, 1)T, (—1,2,1,0)T, (7, —8, —3,2)T linearly indepen- dent in R4? Substantiate your answer. (ii) Find the vector in span ((2, —1,0, 1)T, («1,2, 1,0)T, (7, —8, —3,2)T) that is closest to (1, —1,0,2)T in R4. Substantiate your answer. 1 5 .-—1 O 2 4 1 -1‘ 4. Let B — 0 0 _7 _4 O 0 3 1 Find (i) the eigenvalues of B, (ii) the eigenspace associated with the largest eigenvalue of B. Course Code 7H E £53152 : ..........MA..TZ3.1,.0AN.,&."MATZBl.0.B.......i.,i...., % 2 E (at- :l. E) Page 20f 2 5. Use the following data of seven papers: 9111. Frequence of key words Keywords Papers P3 P4 P5 P6 P7 0 2 "U H "U [Q determinant eigenvalues linear matrices functions orthogonality spaces vectors OWNOBOBUIO‘JO pr-ROTOKIVD-OOO‘J phU‘CDMOOHAKIOJ OOO)OOO©O1#>O and search for the key words orthogonality, eigenvalues, matrics, giving the key word orthogonality twice the weight of the other two key words. Which of the seven papers best matches the search criteria? Substantiate your answer. End of Paper ...
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## MAT2310B_04 - \$&amp;quot;E 9%:— E) Pagelof2 7,52 5% a}: X...

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