Question: Determine whether the statement below is true or false. Justify the answer. If A is a 3 x 2 matrix, then the transformation x-Ax cannot

Determine whether the statement below is true or false. Justify the answer. If A is a 3 x 2 matrix, then the transformation x-Ax cannot be one-to-one. Choose the correct answer below. O A. The statement is false. A transformation is one-to-one if each vector in the codomain is mapped to by at most one vector in the domain. If Ax = b does not have a free variable, then the transformation represented by A is one-to-one. O B. The statement is false. A transformation is one-to-one if each vector in the codomain is mapped to by at most one vector in the domain. It does not matter what dimensions a vector is as long as it meets this requirement. The matrix A could be 1 x4 and still represent a one-to-one transformation. O C. The statement is true. Transformations which have standard matrices which are not square cannot be one-to-one nor onto because they do not have pivot positions in every row and column. O D. The statement is true. A transformation is one-to-one only if the columns of A are linearly independent and a 3 x2 matrix cannot have linearly independent columns

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!

Find a vector x whose image under T, defined by T(x) = Ax, is b, and determine whether x is unique. Let A = Find a single vector x whose image under T is b. x= Is the vector x found in the previous...

A is an n xn matrix. Determine whether the statement below is true or false. Justify the answer. Finding an eigenvector ofA may be difficult, but checking whether a given vector u is in fact an...

Determine whether the statement below is true or false. Justify the answer. The solution set of the linear system whose augmented matrix is [ a 1 a 2 a 3 b ] is the same as the solution set of the...

Write the solution set of the given homogeneous system in parametric vector form. 2x1 + 2x2 + 4x3 = 0 - 4x1-4x2 - 8x3 = 0 where the solution set is x = x2 X3 - 5x2 +10x3 = 0 x=x3 (Type an integer or...

Review Chapter 1 (Q10,12) 5. Use the graph of the function fshown to the right to answer parts (a)-(n). (a) Find r( - 21) and ts). f= E i6): E (b) Find 1 a) and 0). m): |:| fw>= |:| (C) Is f(6)...

SOLVE IT 1.1: Which of the following is always true for any sets A and B ? a) AB=AB b) AB=AB c) AB=AB d) AB=BA e) None of the above 1.2: The inverse of function f(x)=x5+2 is a) f1(x)=(x+2)1/5 b)...

I do not understand this Determine whether the statement below is true or false. If it is false, rewrite it as a true statement. 7 05 =72 Choose the correct answer below. O A. This statement is...

Determine whether the statement below is true or false. If it is false, rewrite it as a true statement. 7C5=7C2 Choose the correct answer below. O A. This statement is false. A true statement is 2C7...

1. A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a king or eight. (b) Compute the probability of randomly selecting...

Determine whether the statement below is true or false. If it is false, rewrite it as a true statement. A combination is an ordered arrangement of objects. Choose the correct answer below. 0 A. The...

Taxpayer A, participated in day-trading throughout the 2021 tax year, including many short sales. A relies on his on-line trading platform to keep track of As stock, sales, dividends and interest...

Design on R.C. column footing with following data. Size of column = 400 rnm x 400 mm. Safe bearing capacity of soil = 200 kN/m2. Load on column= 1400 kN. Concrete M20 and steel Fe 415 is used....

An instrument representing an interest in real property created to secure repayment of the debt is called a: a . foreclosure. b . default judgment. c . mortgage. d . warranty deed.

As part of the initial investment, Jackson contributes accounts receivable that had a balance of $37,457 in the accounts of a sole proprietorship. Of this amount, $1,421 is deemed completely...