Free solutions to linear equation forms - PlainMath

Recent questions in Forms of linear equations

Susan Nall 2021-12-19 Answered

What is the geometric meaning of singular matrix
Could anyone help explain what is the geometric meaning of singular matrix ? What's the difference between singular and non-singular matrix ? I know the definition, but couldn't understand it very well.

Julia White 2021-12-19 Answered

Expressing the determinant of a sum of two matrices?
Can \(\displaystyle{\det{{\left({A}+{B}\right)}}}\)
be expressed in terms of
\(\displaystyle{\det{{\left({A}\right)}}},{\det{{\left({B}\right)}}},{n}\)
where A,B are \(\displaystyle{n}\times{n}\) matrices?
I made the edit to allow n to be factored in.

rheisf 2021-12-18 Answered

Can someone show me step-by-step how to diagonalize this matrix? I'm trying to teach myself differential equations + linear algebra, but I'm stumped on how to do this. I'd really appreciate if someone would take the time to do this with me!
\[\begin{bmatrix}1 & 2&0 \\2 & 1&0\\ 0&0&-3 \end{bmatrix}\]

nemired9 2021-12-17 Answered

Physical meaning of the null space of a matrix
What is an intuitive meaning of the null space of a matrix? Why is it useful?
I'm not looking for textbook definitions. My textbook gives me the definition, but I just don't "get" it.
E.g.: I think of the rank r of a matrix as the minimum number of dimensions that a linear combination of its columns would have; it tells me that, if I combined the vectors in its columns in some order, I'd get a set of coordinates for an r-dimensional space, where r is minimum (please correct me if I'm wrong). So that means I can relate rank (and also dimension) to actual coordinate systems, and so it makes sense to me. But I can't think of any physical meaning for a null space... could someone explain what its meaning would be, for example, in a coordinate system?

2021-12-09

how to find Form a quadratic equation that passes through the following points:

(0, 0), (2, 0) and (-1, 3)

(3, 0), (– 4, 0) and (0, –12)

Monincbh 2021-12-02 Answered

If the Wro
ian W of f and g is \(\displaystyle{3}{e}^{{{4}{t}}}\), and if \(\displaystyle{\left({t}\right)}={e}^{{{2}{t}}}\), find g(t).

Line 2021-10-06 Answered

\(5y+3=2y-3x+5\)
\(y =\) ___

foass77W 2021-10-02 Answered

Find \(6^3 \times 6^{-2}\)

arenceabigns 2021-09-30 Answered

\((792)(5.19 \times 10^-5)\)

Wribreeminsl 2021-09-30 Answered

Suppose that the augmented matrix for a system of linear equations has been reduced by row operations to the given row echelon form. Solve the system by back substitution. Assume that the variables are named\( x_1,x_2,…\) from left to right.
\(\begin{bmatrix}1&-3&7&1 \\0&1&4&0\\0&0&0&1 \end{bmatrix}\)

glamrockqueen7 2021-09-30 Answered

Write the vector form of the general solution of the given system of linear equations.
\(x_1+4x_4=0\)
\(x_2−2x_4\)

Dottie Parra 2021-09-29 Answered

Solve the system by clennaton

\(\begin{cases}2x-y=0\\3x-2y=-3\end{cases}\)
The solution is____

nicekikah 2021-09-29 Answered

Suppose that the augmented matrix for a system of linear equations has been reduced by row operations to the given reduced row echelon form. Solve the system. Assume that the variables are named \(x_1,x_2,\)… from left to right.

\(\begin{bmatrix}1&0&0&-7&8 \\0&1&0&3&2\\0&0&1&1&-5 \end{bmatrix}\)

melodykap 2021-09-29 Answered

Reduce the system of linear equations to upper triangular form and solve.
x+2y=3
4y+2x=6

aflacatn 2021-09-29 Answered

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution.

\(\begin{bmatrix}1&-2&0&-4\\0&0&1&3\\0&0&0&0\end{bmatrix}\)

illusiia 2021-09-29 Answered

Reduce the system of linear equations to upper triangular form and solve.
\(\begin{cases}3x−y=1\\−3x+y=4\end{cases}\)

remolatg 2021-09-28 Answered

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution.

\(\begin{bmatrix}1&-2&6 \\0&0&0 \end{bmatrix}\)

Jaya Legge 2021-09-27 Answered

Consider a consistent system of three linear equations in three variables. Discuss the nature of the system and its solution set if the reduced form of the augmented coefficient matrix has
A) One leftmost 1
B) Two leftmost 1's
C) Three leftmost 1's
D) Four leftmost 1's

permaneceerc 2021-09-27 Answered

The row echelon form of a system of linear equations is given.
(a)Writethesystemofequationscorrespondingtothegivenmatrix.Use x,y.or x,y,z.or \(x_1,x_2,x_3,x_4\) asvariables.
(b)Determinewhetherthesystemisconsistentorinconsistent.Ifitisconsistent,givethesolution. \(\begin{bmatrix}1&-3&|&-4\\0&1&|&0 \end{bmatrix}\)

Carol Gates 2021-09-27 Answered

Determine whether the statement is true or false. If the last row of the reduced row echelon form of the augmented matrix of a system of linear equations has only one nonzero entry, then the system is inconsistent.

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