linear algebra

If A is a nonsingular matrix, what is the null space of A?

If A is nonsingular then the equation:

A x = y

has a unique solution. Now, the equation:

A x = 0

always has a solution:

x = 0.

If A is nonsingular, then this must thus be the only solution. This means that the null space of A is the zero dimensional vector space containing only the null vector 0.

  1. 👍 0
  2. 👎 0
  3. 👁 96
asked by chris

Respond to this Question

First Name

Your Response

Similar Questions

  1. Linear Algebra

    Fnd the left null space of matrix A = [5 -3 1] [-2 4 -6] [11 -8 5]

    asked by Sharon on March 17, 2014
  2. math,algebra II

    I have to work with these types of problems dealing with matrises can someone show me how to solve them.Heres one of them: Directions: Find the values of the variables in each equation in the first matrix it looks like this a+2

    asked by jas on June 6, 2007
  3. matric

    Let matrix p= [6 -4] 1 0 If where a and b are real numbers, I is a identity matrix and 0 is a null matrix, find a and b.

    asked by siti on December 2, 2012
  4. math

    If A^TA is an invertible matrix, prove that the column vectors of A are linearly independent. You know that if statement X implies statement Y then that is equivalent to Not(Y) implies Not(X). You can start by taking the column

    asked by mathstudent on January 8, 2007
  5. College Algebra

    Consider the following Matrix: A= [-2 0 1 -1 -2 1 1 -1 0 ] Choose the correct description of A. Find A−1 if it exists. Multiple Choice homework question: 1) A is Nonsingular; that is, it has an inverse. A^-1= 2) A is singular;

    asked by Moses on February 1, 2017
  1. Algebra II -Please help

    Assign each letter and a blank space to a number as shown by the alphabet table. 0=_ 1=A 2=B 3=C 4=D 5=E 6=F 7=G 8=H 9=I 10=J 11=K 12=L 13=M 14=N 15=O 16=P 17=Q 18=R 19=S 20=T 21=U 22=V 23=W 24=X 25=Y 26=Z use matrix [1 -2] -3 7

    asked by Cassie on April 7, 2014
  2. Algebra

    Consider the following matrix. A = 7, -5 -4, 3 Choose the correct description of A Find A^−1 if it exists. Answer either Choice 1, or Choice 2: CHOICE 1: A is nonsingular; that is, it has an inverse. A^-1 = _________ or CHOICE 2

    asked by Shelby on March 17, 2017
  3. Math

    Hi! I need help with these two questions. Thanks! :) 1.) Can we multiply the Matrix A (which is 3 x 4 matrix) by the other matrix, Matrix B (which is 3 x 4 matrix)? True Or False? 2.) When we multiply the 6 x 3 matrix by the 3 x 1

    asked by Emily on March 26, 2015
  4. Lin. Alegra Help

    Suppose that you are given the following system of linear equations [variables are x1, x2, x3 and x4] x1 + 3x2 + 9x3 + 2x4 =5 x1 + 3x3 - 4x4 =5 x2 + 2x3 + 3x4 =-1 -2x1 + 3x2 + 5x4 =-1 Let b be the vector such that B = [A b] , and

    asked by V. on May 16, 2007
  5. science

    1 A ……... is a rectangular array of numbers that are enclosed within a bracket . horizontal set vertical matrix 2 When the numbers of rows is equal to the numbers of columns equal to 'n'. Where m=n. Then is

    asked by sunday on March 15, 2014

More Similar Questions