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You can solve a system of equations by translating it into a matrix manipulating the matrix until it has eliminated terms and then translating it back to equations?
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∙ 13y ago
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When will a system of linear equations be inconsistent?
When the matrix of coefficients is singular.
What is B called in the matrix representation of a system of linear equations when written as AX equals B?
A = coefficient matrix (n x n) B = constant matrix (n x 1)
How do you solve these matrix word problems that involve equations?
Well, it's important to ask the question first.
How can a system of linear equations be represented as a matrix equations?
Here is a simple way to see it that will help you both understand and remember. Take two equations in two unknowns. You can generalize later. Make a 2x2 matrix using the coefficients only. Now if you multiply this equation by the vector (x,Y) written as a column and placed on the right side of the matrix and you have the 2 equations you started with. Now put the constants, that is to say what each equation is equal to, on the right side of the = sign. If you invert the coefficient matrix on the left, the 2x2 one, and multiply both sides by that inverse, the equation is solved. There is another method known as Cramer's rule that can help you to solve equations using matrices. I suggest you look that one up if you are interested or ask for some more help!
What is cut set matrix in graph theory?
Cut Set matrix provides a compact and effecive means of writing algebriac equations giving branch voltages in terms of tree branches.
How do you solve 4 equation with 4 unknows?
Create a matrix of the coefficients of each equation. The solutions to the equations should make up the rightmost column of the matrix. Then, row reduce the matrix until you are able to rewrite the equations and solve them. The matrix should be a 4x5 matrix (4 rows and 5 columns) for four equations with four variables. This is known as a system of equations.
Is formed from the constant in a system of equations?
constant matrix
Which best describes a system of equations that has no solution?
An "inconsistent" set of equations. If they are all linear equations then the matrix of coefficients is singular.
When will a system of linear equations be inconsistent?
When the matrix of coefficients is singular.
What makes a system of equations dependent?
If one (or more) of the equations can be expressed as a linear combination of the others. This is equivalent to the statements the matrix of coefficients does not have an inverse (or is singular), or the determinant of the matrix of coefficients is zero.
Examples of nullity of a matrix?
A null matrix is a matrix with all its elements zero.EXAMPLES : (0 0) is a null row matrix.(0 0)(0 0) is a null square matrix.NOTE : Text handling limitations prevent the printing of large brackets to enclose the matrix array. Two pairs of smaller brackets have therefore been used.Answer 2:The above answer is a null matrix. However, the nullity of a matrix is the dimension of the kernel. Rank + Nullity = Dimension. So if you have a 4x4 matrix with rank of 2, the nullity must be 2. This nullity is the number of "free variables" you have. A 4x4 matrix is 4 simultaneous equations. If it is rank 2, you have only two independent equations and the other two are dependent. To solve a system of equations, you must have n independent equations for n variables. So the nullity tells you how short you are in terms of equations.
How do you solve 3 dimensional equations?
You can solve the system of equations with three variables using the substitute method, or using matrix operations.
An array of numbers where each row contains the numbers from one of the equations?
matrix
Is an array of numbers where each row contains the numbers from one of the equations?
matrix
What does it means if there are an infinite number of solutions to a system of equations?
In simple terms all that it means that there are more solutions than you can count!If the equations are all linear, some possibilities are given below (some are equivalent statements):there are fewer equations than variablesthe matrix of coefficients is singularthe matrix of coefficients cannot be invertedone of the equations is a linear combination of the others
What is B called in the matrix representation of a system of linear equations when written as AX equals B?
A = coefficient matrix (n x n) B = constant matrix (n x 1)
How can systems of equations be solved?
It depends on your level of expertise. The simplest method is to invert the matrix of coefficients.
