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  3. 1 let u 583 v 885 and w 90 9...

Question: 1 let u 583 v 885 and w 90 9...

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1. Let u (5,8,3), v (8,8,-5), and w (9,0, 9). Find 4u +5v- w. 2. Find the vector v for which v u+4wgiven that u2,9) and w (-5,-2) 3. Provided that u=(23) and w=(4,-3),writev-(26,3) as a linear combination of u and w, ifpossible. 4. Determine whether s (8,4,3),(0,4,3),(0,0,3) is a basis for R3. If it is, write u (40,8,15) as a linear combination of the vectors in S 5. Find a basis for the column space of the matrix 6. Find a basis for the subspace of R3 spanned by s (42,30,54),(14,10, 18),(7,5,6). 7. Given that [xlB [4,5,3, the coordinate matrix of x relative to a (nonstandard) 8 16 basis B [1,1,0),(1,0,1),(0,0,0)). Find the coordinate vector of x relative to the standard basis in R3. 8. Find the coordinate matrix of x -(-3,28,6) in R3 relative to the basis B (3,8,0),(5,0,1 1),(1,5,7). 9. Find the transition matrix from B- ((1,7),(-2, -2))to B [(-28,0),(-4,4)) 10 Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the conic defined by the function 13x2 + 13y2+10xy-36-0.

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