1,975 Answered Questions for the topic linear algebra

Linear Algebra

11/02/21

A linear Algebra question

Let V be a finite-dimensional vector space over an algebraically closed field F.Suppose A is a commutative subalgebra of L(V, V ), i.e. if S, T ∈ A, and c ∈ F then• S + T ∈ A,• ST ∈ A,• cT ∈ A,... more
Linear Algebra

10/29/21

T/F: If A has full row rank, then AA^T must be invertible.

If A has full row rank, then AA^T must be invertible. True or False?
Linear Algebra Proofs

10/29/21

Show that u and v are orthogonal if and only if (||u+v||)^2 = ||u||^2+||v||^2.

Show that u and v are orthogonal if and only if (||u+v||)^2 = ||u||^2+||v||^2.
Linear Algebra Math

10/27/21

Math test question

On a certain test there are two types of questions – multiple choice questions worth 2 marks each and short answer questions that are worth 5 marks each. The test is out of a total of 64 marks. How... more
Linear Algebra

10/27/21

For each question below, indicate whether the statement is true or false. If it is true, explain why. If it is false, provide a counter-example.

a. (2 points) True or False: If x is a vector in the null space of A then x will also be in the null space of M = AB. b. (2 points) True or False: If x is a vector in the null space of B then x... more
Linear Algebra

10/20/21

Find the smallest solution for which all four variables are positive integers

5x+ y+ z=K x+7y+ z=K x+ y+8z=K a. Express Equations (5) as a homogeneous linear system of three equations in four unknowns (x, y, z, and K), and show that the solution set has one arbitrary... more
Linear Algebra

10/18/21

Let’s consider the subspace of a vector space of all functions of a variable t.

a) what are the coordinates of the function 3 sin t + 5 cos t = f(t) with respect to the basis {sin t, cost}?b) Find coordinates with respect to base {cos t, sin t}
Linear Algebra Algebra Matrix Matrices

10/17/21

Matrices question

Hi I'm am struggling to answer the last question in my textbooks chapter...Three crop sprays are manufactured by combining chemicals A, B and C as follows:One barrel of spray P contains 1 unit of... more
Linear Algebra Math Mathematics

10/14/21

Math Linear Algebra help

Find equations for all the planes that intersect the y-axis at y = 1 and the z-axis at z = 2, and are tangent to the sphere (𝑥 − 2)^2 + 𝑦^2 + 𝑧^2 = 4. You cannot use calculusPlease help and if you... more
Linear Algebra Math Algebra 1 Algebra 2

10/09/21

Name any two points on a horizontal line that is 8 units above the x-axis. (Enter your answers as a comma-separated list of ordered pairs.)

Name any two points on a horizontal line that is 8 units above the x-axis. (Enter your answers as a comma-separated list of ordered pairs.)
Linear Algebra Math Algebra 1 Algebra 2

10/09/21

Write as an ordered pair the coordinates of the point whose y-coordinate is 5 and whose x-coordinate is −2.

Write as an ordered pair the coordinates of the point whose y-coordinate is 5 and whose x-coordinate is −2.
Linear Algebra

10/07/21

Find general solution for the system of linear equations

2x+4y+z=3x+2y+2z=3x+2y+z=2
Linear Algebra

10/05/21

compute the following. If an answer does not exist, enter DNE.

Let A= [ 5 ] [ 1 ] [ 5 ]If possible, compute the following.A^TA=AA^T=
Linear Algebra

10/01/21

linearly dependent set

Let be a linearly independent set.Which of the following sets are linearly dependent?1) {u+v,4u+4v}2) {6u,6v}3) {u,0}4) {u,u+v}
Linear Algebra Functions

09/30/21

Writing equations of lines parallel and perpendicular to a given line through a point

Consider the line 4x+2y=-6.Find the equation of the line that is parallel to this line and passes through the point (4,4).Find the equation of the line that is perpendicular to this line and passes... more
Linear Algebra Geometry Algebra

09/29/21

How to find the geometric description of the system of equation?

For example, -x + y - 3z = -3x - y - 2z = 25x - 5y - 5z = 12How do I know if it is:a. three planes intersecting in a lineb. three planes with no common intersectionc. three planes intersecting at a... more

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