In Exercises 11 – 15 which of the sets S are subspaces? 11. S= {(a, b, c) E R° : a > 0, b > 0, c > 0}. {(x1, x2, x3) E R° 0 where a1, a2, a3 E R are fixed}. 12. S = a1x1 + a2x2 + a3x3 : R² {(x, y) (x, y) is on the line through (1, 1) with slope 1}. 13. S :

Q: Q7 Define the matrix for the linear mapping that reflects a planes dots in the line 4x+ 3y = 0.

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Q: One of the following vectors lies in span{ 2+x + x?, 3+x- 2x2} (A) 4+ x – 7r² (B) 4+ x – 4x? (C) 4 +…

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Q: a.Give the R code to assign the values in in the len column of ToothGrowth to the vector named x.…

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Q: Describe geometrically (line, plane, or all of R 3) all linear combinations of (a) [ 1/2/3 ] and […

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Q: Find the coordinate vector of x2 + x - 17 relative to the basis {x² + 1, x + 2, x - 3}.

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Q: The two open disks B((1,2);2) and B((-2,1);1) has intersection. True or False

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Q: _et a₁ = -1 a₂= -7 -7 3 and b = 3 -15 h For what value(s) of his b in the plane spanned by a, and a

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Q: The two open disks B((1, 2); 2) and B((-2, 1); 2) has intersection. True False

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Q: Each week a builder makes an order of doors from a supplier. The doors normally cost $60 each, but…

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Q: Solve step by step in digital format please Do the x³2x²+1, 4x² − x+3,3x-2y-2x³+4x² - 2 polynomials…

A: This is the question from the vector space.

Q: 5а+ 2b Decide whether the set of all vectors of the form is a subspace of R³ or a

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Q: Is A = diagonalizable. Justify your conclusion. 10 120 -3 5 2,

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Q: In a vector space of dimension 5, every set of 6 vectors would span the vector space.

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Q: Question 2: For which real values of a do the polynomials P1(t) = at? -t-; P2(t) = - + at -; P3(t) =…

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Q: how can one check that a set is LI or LD? if a set contains the zero vector, can it be LI? why?

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Q: Are all functions from one vector space to another linear?

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.