You are watching: Is u in the plane in set of real numbers rℝcubed3 spanned by the columns of a? why or why not?
False, because the summary applies to a solitary solution. The solution set consists of all feasible services.
Is the statement "Two standard concerns about a linear device involve existence and uniqueness" true or false? Exsimple.
True, bereason two basic inquiries deal with whether the solution exists and also whether tbelow is only one solution.
Is the statement "Two matrices are row identical if they have the exact same number of rows" true or false? Explain.
False, because if 2 matrices are row tantamount it indicates that tright here exists a sequence of row operations that transforms one matrix to the various other.
Is the statement "Elementary row operations on an augmented matrix never change the solution collection of the linked linear system" true or false? Exsimple.
Is the statement "Two tantamount direct units deserve to have actually various solution sets" true or false? Exordinary.
Is the statement "A continuous system of direct equations has one or more solutions" true or false? Explain.
In some instances, a matrix may be row diminished to even more than one matrix in decreased echelon develop, utilizing various sequences of row operations.
The statement is false. The algorithm uses to any matrix, whether or not the matrix is regarded as an augmented matrix for a straight device.
A basic variable in a direct system is a variable that synchronizes to a pivot column in the coreliable matrix.
Finding a parametric description of the solution set of a straight device is the exact same as addressing the mechanism.
The statement is false. The solution set of a direct system have the right to just be expressed using a parametric description if the mechanism has at leastern one solution.
If one row in an echelon develop of an augmented matrix is left bracket Start 1 By 5 Matrix 1st Row 1st Column 0 2nd Obelisk 0 3rd Pillar 0 4st Tower 5 5st Shaft 0 EndMatrix best bracket , then the connected linear system is incontinuous.
The statement is false. The suggested row synchronizes to the equation 5x 4equals0, which does not by itself make the device inconsistent.
The statement is false. The echelon form of a matrix is not distinctive, but the reduced echelon form is distinct.
The pivot positions in a matrix depend on whether row intertransforms are provided in the row reduction process. Choose the correct answer below.
The statement is false. The pivot positions in a matrix are determined entirely by the positions of the leading entries in the nonzero rows of any type of echelon create derived from the matrix.
Reducing a matrix to echelon form is called the forward phase of the row reduction process. Choose the correct answer below.
The statement is true. Reducing a matrix to echelon develop is called the forward phase and also reducing a matrix to reduced echelon form is called the backward phase.
Whenever before a mechanism has actually free variables, the solution collection includes many kind of options. Choose the correct answer listed below.
The statement is false. The presence of at least one solution is not related to the presence or absence of cost-free variables. If the mechanism is incontinuous, the solution collection is empty.
A general solution of a device is an explicit description of all services of the device. Choose the correct answer below.
The statement is true. The row reduction algorithm leads directly to an explicit summary of the solution set of a straight device once the algorithm is used to the augmented matrix of the mechanism, causing a general solution of a mechanism.
A straight device is constant if and only if the rightmost column of the augmented matrix_____________a pivot column. That is, if and just if an echelon form of the augmented matrix has_____________ of the form <0 ... 0 b> with b nonzero.
Suppose the coreliable matrix of a mechanism of direct equations has a pivot place in eexceptionally row. Explain why the device is consistent.
The system is regular because the rightmany column of the augmented matrix is not a pivot column.
The points in the plane matching to <-2; 5> and <-5; 2> lie on a line via the origin. Choose the correct answer listed below.
False if <-2; 5> and <-5; 2> were on the line via the origin, then <-5,2> would certainly be a multiple of <-2;5>.
An example of a linear combination of vectors v1 and v2 is the vector (1/2) v1. Choose the correct answer listed below.
The solution set of the linear system whose augmented matrix is
The set Span u,v is always visualized as a plane through the origin. Choose the correct answer below.
False. This statement is often true, but Span u,v is not a plane as soon as v is a multiple of u or as soon as u is the zero vector.
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When u and also v are nonzero vectors, Spanu,v consists of only the line via u and also the line through v and also the beginning.