MATH 461 Midterm: MATH461 BOYLE-M SUMMER I2006 0101 MID EXAM 1

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turquoisegnu128

15 Feb 2019

School

University of Maryland

Department

Mathematics

Course

MATH 461

Professor

All

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Document Summary

Math 461-0101 summer 2006 exam 2. Put a box around your nal answer to each part. Show all work: (16 points) put the matrix. 0 8 2 4 6 into row echelon form. Justify your answer: (9 points) let v be a nite dimensional vector space with dimension greater than zero. Suppose that there are at least 3 linearly independent vectors x such that ax = 0. A which are linearly independent, but there are not k + 1 columns which are linearly independent. Clearly justify your answer: (10 points) let v be the vector space of polynomials of the form a0 + a1x + a2x2. Determine whether { 1+2x+3x2, 4+5x+6x2, 5+4x+3x2 } is a linearly independent subset of v . Show work: (10 points) suppose that b = {b1, b2} and c = {c1, c2} are two bases for a vector space. V , with b1 = 2c1 + c2 and b2 = 4c1 + c2.

Related Questions

4. (12 points) Let the matrix A and its reduced row echelon form R be given by the following. A= [ 1 -2 2 -3 1 -2 4 -1 4 1 -3] [1001 1] -4 0 0 1 0 1 1 7 -1 0 0 1 1 -1 | = R. (a) Find a basis for the column space of A. (b) Find a basis for the row space of A. (c) Find a basis for the null space of A. (d) Verify that the dimension of the column space of A plus the dimension of the null space of A is equal to the number of columns of A.

This is linear algebra.