Mathematics

Mathematics, 26.07.2019 17:30, faithyholcomb

What does it mean for rows to be linearly independent?

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Mathematics, 29.06.2019 03:30, jfrey7621

(25 points) mark as true or false; no justification necessary. (a) if a and b are n × n-matrices such that ab has linearly inde pendent columns, then a has linearly independent columns. (b) there is a linear transformation t : r7 ? r3 with two- dimensional kernel. (c) there is a set of four vectors which span r5. (d) if the columns of a n x n-matrix a are linearly independent, then so are the rows of a. (e) the set of polynomials p(t) satisfying p(1) 5 is a subspace of p5. (f) the set of vectors of the form (2x-y+z,r+3z,2u-77 - y -z -1) is a subspace of r4 e sum of the dimensions of the row space and the null space of a equals the number of rows of a. (g) th (h) the non-pivot columns of a matrix are always linearly de (i) if h pen- ace of r3, then there is a 3 x 3-matrix with ce v of 3 x 4-matrices contains a spanning set dent. is a subsp h col a. of 13 vectors.

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Mathematics, 10.07.2019 02:20, 23ricorvan

1. label the following statements as true or false. a. an injective linear map t : u ? v maps linear independent vectors to linearly independent vectors. b. any set of linearly independent vectors vi,v2, ,vk n rn can be extended to a basis by adding n- kunit vectors c. any subspace of r" is the solution-space of a linear system ax-0. d. elementary row operations on an m x n-matrix a don't change the space generated by the columns of a e. elementary row operations on an m x n-matrix a don't change the space generated by the rows of a f. a linear system ax- 0 of m -equations in n-unknowns has always a nontrivial solution ifnnm g. if an m x n-matrix a has r-many linearly independent rows than it also must have n many linearly independent columns h. the determinant function det is a linear function on the vector space of n x n-matrices l. let a be an n × n-matrix. then det(cd) c det(a). j. for any n x n-matrix a one has that det(a"(a) (a" 1s the transpose ofa.)

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Mathematics, 20.07.2019 02:20, kennettahughley7964

Suppose a is a 4 x 7 matrix such that rank(a = 4. which of the following is true? a. the rank of at is 3 b. the nullity of a^t is 0 c. ax 0 only has trivial solution d. the rows of a are linearly dependent columns of a are e. linearly independent

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Mathematics, 07.11.2019 02:31, st23pgardner

Each statement that follows is either true (in all cases) or false (for at least one example). if false, construct a speciﬁc example to show that the statement is not always true. such an example is called a counterexample. if true, give a justiﬁcation. a. if v1, v2, v3, v4 are in r4 and v is not a linear combination of v1, v2, v4 then {v1, v2, v3, v4} is linearly independent. b. if v1, v2, v3, v4 are in r4 and {v1, v2, v3} is linearly dependent then {v1, v2, v3, v4} is also linearly dependent. c. if v1, v2, v3, v4 are linearly independent vectors in r4 then {v1, v2, v3} is also linearly independent.

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