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Linear Algebra With Applications (classic Version)
- 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
- Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry requires $0.30 of coal and $0.70 of steel. Every $1 produced by steel requires $0.80 of coal and $0.20 of steel. Find the annual production (output) of coal and steel if the total annual production is $20 million.arrow_forwardShow that the three points (x1,y1)(x2,y2) and (x3,y3) in the a plane are collinear if and only if the matrix [x1y11x2y21x3y31] has rank less than 3.arrow_forwardThe rows of AB are linear combinations of the rows of B. This means that the row space of AB is contained in, and is possibly equal to, the row space of B. Give an example A and B where the row spaces of BB and AB are not equal. Show your work.arrow_forward
- A 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_forwardIf 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_forwardShow R³ is a banach space.arrow_forward
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