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Linear Algebra With Applications
- Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)arrow_forwardFind all subsets of the set S={(1,3,2),(4,1,1),(2,7,3),(2,1,1)} that form a basis for R3.arrow_forwardLet T be a linear transformation from R2 into R2 such that T(4,2)=(2,2) and T(3,3)=(3,3). Find T(7,2).arrow_forward
- What operations can be performed on a linear system to arrive at an equivalent system?arrow_forwardLet B={(1,-2,1), (4,-7,5), (5,-8,8)), and x=(-6,10,-7) Find [x]B Give your answer in the form (a,b,c) with no spacesarrow_forwardSuppose that in a biological system there are n species of animals and m sources of food. Let ï¿ represent the population of the jth species, for each j = 1, . . ., N; let bi represent the available daily supply of the ith food; and let aÿj represent the amount of the ith food consumed on average by a member of the jth species. The linear system a11x1 + a12X2 + + A1n xn b₁, a21x1 + a22x2 + + A2n xn : b2, am1x1 + am 2x2 + represents an equilibrium A. Let A = [aij] - = = ⠀ : bm + Amn Xn where there is a daily supply of food to precisely meet the average daily consumption of each species. = 1 2 0 3 = " 1 0 2 2 X = (xj) = [1000, 500, 350, 400], and b 0 0 1 1 (bį) = [3500, 2700, 900]. Is there sufficient food to satisfy the average daily consumption? (Hint: The linear system holds if Ax b. We don't exactly need this, but think about how the entries in Ax should be compared to those of b.) B. What is the maximum number of animals of species 1 that could be added to the system with the supply…arrow_forward
- If R = {(1, 2), (1, 4), (2, 3). (3, 1), (4, 2)}, what is the symmetric closure of R? O {(1, 2), (2, 1), (1, 4), (4, 1), (2, 3), (3, 2), (3, 1), (1, 3), (4, 2), (2, 4)} O {(1, 1), (1, 2), (1, 4), (2, 2), (2, 3), (3, 1). (3, 3), (4, 2), (4, 4)} O {(1, 2), (1, 4), (2, 3), (3, 1), (4, 2)} O {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1). (3, 2). (3, 3), (3, 4), (4. 1), (4, 2), (4, 3), (4, 4)}arrow_forwardA group of 4 students namely Maiyra, Bansan, Kate and Davis from final semester in Computer Sciences Department have to choose from 3 majors namely, DIP, Computer Vision and Pattern Recognition offered by the Department. i. Specify relation RCAXB as the set that lists all students a e A enrolled in class of that major be B ii. Determine the Diagraph and Matrix Representation for the given relation R: R=(Mayra, DIP),(Bansan, Computer Vision).(Bansan, Patten Recognition),(Davis, Computer Vision),(Davis, DIP))arrow_forwardShow R³ is a banach space.arrow_forward
- If the set A has 3 elements and the set B = {3, 4, 5}, then find the number ofelements in (A×B).arrow_forwardWrite out the elements of the set 2* where X = {1,{0},Ø, {2,3}}.arrow_forwardThe conditions for affine dependence are stronger than those for linear dependence, so an affinely dependent set is automatically linearly dependent. Also, a linearly independent set cannot be affinely dependent and therefore must be affinely independent. Construct two linearly dependent indexed sets S1 and S2 in R2 such that S1 is affinely dependent and S2 is affinely independent. In each case, the set should contain either one, two, or three nonzero points.arrow_forward
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