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How do you add fractions in matrices?
The usual rules of addition of fractions apply.
Is the set of all 2x2 invertible matrices a subspace of all 2x2 matrices?
I assume since you're asking if 2x2 invertible matrices are a "subspace" that you are considering the set of all 2x2 matrices as a vector space (which it certainly is). In order for the set of 2x2 invertible matrices to be a subspace of the set of all 2x2 matrices, it must be closed under addition and scalar multiplication. A 2x2 matrix is invertible if and only if its determinant is nonzero. When multiplied by a scalar (let's call it c), the determinant of a 2x2 matrix will be multiplied by c^2 since the determinant is linear in each row (two rows -> two factors of c). If the determinant was nonzero to begin with c^2 times the determinant will be nonzero, so an invertible matrix multiplied by a scalar will remain invertible. Therefore the set of all 2x2 invertible matrices is closed under scalar multiplication. However, this set is not closed under addition. Consider the matrices {[1 0], [0 1]} and {[-1 0], [0 -1]}. Both are invertible (in this case, they are both their own inverses). However, their sum is {[0 0], [0 0]}, which is not invertible because its determinant is 0. In conclusion, the set of invertible 2x2 matrices is not a subspace of the set of all 2x2 matrices because it is not closed under addition.
What would be the result if you add matrices B plus A instead A plus B?
It would be no different. Matrix addition is Abelian or commutative. Matrix mutiplication is not.
Do all matrices have determinant?
Only square matrices have a determinant
Under what condition is the product of skew-symmetric matrices skew-symmetric?
I could be wrong but I do not believe that it is possible other than for the null matrix.
What is performing addition subtraction and scalar multiplication of matrices?
Matrix arithmetic
How do you add fractions in matrices?
The usual rules of addition of fractions apply.
When adding or subtracting matrices do the dimensions of the sum or differences always match the original matrices?
Yes, because otherwise addition and subtraction are not defined.
Are matrix addition and matrix multiplication commutative?
Matrix addition is commutative if the elements in the matrices are themselves commutative.Matrix multiplication is not commutative.
How do you develop a JAVA program that computes matrices?
Matrices can't be "computed" as such; only operations like multiplication, transpose, addition, subtraction, etc., can be done. What can be computed are determinants. If you want to write a program that does operations such as these on matrices, I suggest using a two-dimensional array to store the values in the matrices, and use for-loops to iterate through the values.
Propertes of matrices?
Algebraic Properties of Matrix Operations. In this page, we give some general results about the three operations: addition, multiplication.
Is the set of all 2x2 invertible matrices a subspace of all 2x2 matrices?
I assume since you're asking if 2x2 invertible matrices are a "subspace" that you are considering the set of all 2x2 matrices as a vector space (which it certainly is). In order for the set of 2x2 invertible matrices to be a subspace of the set of all 2x2 matrices, it must be closed under addition and scalar multiplication. A 2x2 matrix is invertible if and only if its determinant is nonzero. When multiplied by a scalar (let's call it c), the determinant of a 2x2 matrix will be multiplied by c^2 since the determinant is linear in each row (two rows -> two factors of c). If the determinant was nonzero to begin with c^2 times the determinant will be nonzero, so an invertible matrix multiplied by a scalar will remain invertible. Therefore the set of all 2x2 invertible matrices is closed under scalar multiplication. However, this set is not closed under addition. Consider the matrices {[1 0], [0 1]} and {[-1 0], [0 -1]}. Both are invertible (in this case, they are both their own inverses). However, their sum is {[0 0], [0 0]}, which is not invertible because its determinant is 0. In conclusion, the set of invertible 2x2 matrices is not a subspace of the set of all 2x2 matrices because it is not closed under addition.
Can the elimnation matrices only be applied to square matrices?
Only square matrices have inverses.
How do you add matrices?
You add matrices by adding their respective terms - e.g. the element in the first row and sixth column of the sum is the sum of the elements in the addends' first rows and sixth columns. Wikipedia has a nice example of matrix addition that I linked below.
What would be the result if you add matrices B plus A instead A plus B?
It would be no different. Matrix addition is Abelian or commutative. Matrix mutiplication is not.
How matrices applicable in daily life?
how is matrices is applicable in our life?
What is the singular form of matrices?
The singular form of matrices is matrix.
