Please follow the comment If A is an n×n matrix with the property that Ax =...

Question

Question

Please follow the comment

If A is an n×n matrix with the property that Ax = 0
for all x ∈ Rn, show that A = O. Hint: Let x = ej
for j = 1, . . . , n.

Answer 1

Answer #1

let A (ar,aan) lef ej0 an:o

Answer 2

Similar Homework Help Questions

Please explain with example: follow the comment: If A is an n×n matrix with the property...

Please explain with example: follow the comment: If A is an n×n matrix with the property that Ax = 0 for all x ∈ Rn, show that A = O. Hint: Let x = ej for j = 1, . . . , n. Why ej=(1,....n) then it comes out it is a column vector and all zero except 1 inside, i don't get it Ax = 0 for all XEO" Let A-(a,a,. Let e.-| | | ← jth element...
Please tell me what happen here the question is : If A is an n×n matrix...

Please tell me what happen here the question is : If A is an n×n matrix with the property that Ax = 0 for all x ∈ Rn, show that A = O. Hint: Let x = ej for j = 1, . . . , n Given that A is an n×n matrix with the property AX = 0 for all X " 1 A=(a,,a,, 0 0 Let a.) Let e, =| | | ← ith element Comment
Let A be an m × n matrix, let x Rn and let 0 be the zero vector in Rm. (a) Let u, v є Rn be any two solutions of Ax 0,...

Let A be an m × n matrix, let x Rn and let 0 be the zero vector in Rm. (a) Let u, v є Rn be any two solutions of Ax 0, and let c E R. Use the properties of matrix-vector multiplication to show that u+v and cu are also solutions of Ax O. (b) Extend the result of (a) to show that the linear combination cu + dv is a solution of Ax 0 for any c,d...

please find the null space span for matrix A by Ax=0 show all the step. Matrix...

please find the null space span for matrix A by Ax=0 show all the step. Matrix A is. how many variables here? please follow the comment 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Please follow the comment and explain it step by step Let A be a 2 ×...

Please follow the comment and explain it step by step Let A be a 2 × 2 matrix, and let LA be the linear operator defined by L(x) = Ax Show that (a) L maps R2 onto the column space of A. (b) if A is nonsingular, then LA maps R2 onto R2
please help if you know Optimization with Quadratic Functions Could you please prove 89. Thank you so much ! Qua...

please help if you know Optimization with Quadratic Functions Could you please prove 89. Thank you so much ! Quadratic Functions A quadratic function is a mapping Q R R that is a scalar combination of single variables and pairs of variables. Thus, there are coefficients Cli,] and Ell, and a real number q, such that for X E IRn, we have The m atrix notation for C is suggestive. Indeed, C is n × n, and we take E...

LINEAR ALGEBRA: PLEASE FOLLOW THE COMMENT and please tell me what is the rotate matrix and...

LINEAR ALGEBRA: PLEASE FOLLOW THE COMMENT and please tell me what is the rotate matrix and why there is cos@ and -sin@ i think it should be cos@ and sin@ on the first row For each of the following linear operators on R2, find the matrix representation of the transformation with respect to the homogeneous coordinate system: (a) The transformation L that rotates each vector by 120◦ in the counterclockwise direction (b) The transformation L that translates each point 3...
Matrix notation: A=(a1,a2,a3.....,an) = [a1 a2 a3 a4 .....an] are they equal? look at the sample...

Matrix notation: A=(a1,a2,a3.....,an) = [a1 a2 a3 a4 .....an] are they equal? look at the sample picture A should be matrix but it uses ( ) rather than [ ] Given that A is an n×n matrix with the property AX = 0 for all X " 1 A=(a,,a,, 0 0 Let a.) Let e, =| | | ← ith element Comment
Problem 1 (Linear Systems of Equations). (a) Determine the values of a for which the follow- ing ...

Problem 1 (Linear Systems of Equations). (a) Determine the values of a for which the follow- ing system of equations have no solution, exactly one solution, infinitely many solutions (a + 2)y + (a2-4)2 = (0-2) (b) If A = 4-1 0 a 2b a a be the augmented matrix of a linear system of equations then evaluate the values of a and b for which the linear system has no solution? exactly one solution? one parameter solution? two parameter...

Matrix conception question please able to follow the comment 1. If the nxn matrix has a...

Matrix conception question please able to follow the comment 1. If the nxn matrix has a unique solution, that is invertible. true or false 2. all invertible matrix only has one solution true or false and explain