[1 1 -21 30 1[2 3[1 1 -2-10 20 0 -1Lo o-13-73-745.If matrix A =3-32-1-20 0 0a. Find a basis for Nul A.b. Find a basis for Col A.c. What is the dimension of the null space of A?d. What is the rank of A?

Multipart : We have given a matrix , A = 11-20-1133-73013-32230-20 ~ 11-20-1025-7400-1-1000000…

Answered: [1 1 -2 1 3 0 1 [2 3 -1] [1 1 -2 -1] 3…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section: Chapter Questions

Problem 9RQ

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Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner product p,q=a0b0+a1b1+a2b2+a3b3. An Orthonormal basis for P3. In P3, with the inner product p,q=a0b0+a1b1+a2b2+a3b3 The standard basis B={1,x,x2,x3} is orthonormal. The verification of this is left as an exercise See Exercise 17..
Determine whether S={1t,2t+3t2,t22t3,2+t3} is a basis for P3.
Label each of the following statements as either true or false. Let A be a square matrix of order n over R such that A23A+In=On. Then A1=3InA.
a Find a symmetric matrix B such that B2=A for A=[2112] b Generalize the result of part a by proving that if A is an nn symmetric matrix with positive eigenvalues, then there exists a symmetric matrix B such that B2=A.
For each of the following matrices A in SL(2,R), list the elements of A and give the order | A |. a. A=[ 0111 ] b. A=[ 1110 ]

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[1 1 -2 1 3 0 1 [2 3 -1] [1 1 -2 -1] 3 -7 3 2 -7 5. If matrix A = 0 0 -1 lo o 3 -3 2 -1 -2 a. Find a basis for Nul A. b. Find a basis for Col A. c. What is the dimension of the null space of A? d. What is the rank of A?