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: Draw vector 1/2CD - 2FE

A:

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

A: Given that,

Q: Let B={(1,-2,1), (4,-7,5), (5,-8,8)], and x=(-6,10,-7) Find [x]B

A:

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

A:

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

A: If b is in the plane spanned by a1 and a2 then b can be written as linear combination of  a1 and a2…

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

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: I need help with this assignment. they all should have 4 places after the decimal place unless the…

A: Solution:

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

A:

Q: Let A = -1 -3 3 and b = b₁ 8} Show that the equation Ax=b does not have a solution for some choices…

A:

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

A:

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

A:

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

A: Let f: V→W is a  map from vector  V to W such that fx=x2 The given example the function from one…

Q: De termine if the vectors 2 re lincarly independent or linearly dependent Please explain your answer

A:

Q: Describe all solutions of Ax 0 in parametric vector form, where A is row equivalent to the given…

A:

Q: Give an example of 3 vectors spaces that are not Rn. Explicitly state the definition of addition and…

A:

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.