Question: 2. [6 marks] Let A be an n x n matrix. Show, using the Subspace Test, that null(A) is a subspace of R. Hint: Recall

2. [6 marks] Let A be an n x n matrix. Show, using the Subspace Test, that null(A) is a subspace of R". Hint: Recall that null(A) = D E R3 : Ar = 0 . Use this definition to show that the three criteria of the Subspace Test are satisfied

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

2. [6 marks] Let A be an n x n matrix. Show, using the Subspace Test, that null(A) is a subspace of R". Hint: Recall that null(A) = T E R3 : AT = 0 . Use this definition to show that the three...

7. Let W be a subspace of R". Recall that W! = fu ER" | u is orthogonal to W} is also a subspace of R". (i) [2 marks] Show that WnW = {0}. (ii) [4 marks] Given a basis S = {w1, w2, . . . ,Wm} for W....

Homework 1. Suppose that y is orthogonal to u and v. (a) Show that y is orthogonal to the vector u + v. (b) Show that y is orthogonal to every w in Span {11. v}. (Hint: an arbitrary vector w E Span...

(a) Let A and B be two square matrices of the same dimension and A be an invertible matrix then (A-1BA) 2020 = A-1 B2020 A. O True False Justification: (b) Let A be an n x n matrix. The set of all n...

12:39 1 .0 LTE Done 5 of 5 (3) Let V be the vector space of polynomials of degree at most n. Are the following subspaces? Prove or disprove. (a) All polynomials of the form f(x) = ar", where a is a...

there are part a b c kindly answer all parts a) Show that the matrix rotates/scales the vectors and differently. Draw the vectors and the outputs b) Recall that the length of a vector G is va' +b ....

XYZ What is the difference between volatile and nonvolatile memory? Is RAM volatile or nonvolatile? Is ROM volatile or nonvolatile? 7.9 Registers perform a very important role in the fetch-execute...

Please help me with parts (d) and (e), thanks. Eigenvectors and Diagonalization (a) Let A be an n x n matrix with n linearly independent eigenvectors 71, 72, ..., Un, and corre- sponding eigenvalues...

Select a core business transaction cycle (for example revenues, purchasing, expenditures, payroll, or the general ledger) that is of personal interest to you. For this core business transaction...

In the steady state, the government benefits from inflation. Explain.

La empresa FERJOSOF EIRL ha producido en el mes en curso 1,080 unidades del producto: "Jeans para damas" por un costo de produccin de S/. 86,400.00. Durante el periodo vende 920 unidades a un precio...

On 1 March 2007 DB Limited issued R560 000 15% debentures at R98. The debentures were to be redeemed at par in four equal annual payments starting 28 February 2010. Required: Journalise the above...