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The two matrices and their answer must be of the same dimensions.
Each element of the answer matrix is the sum of the elements in the corresponding elements on the matrices that are being added.
In algebraic form,
if A = {aij} where 1 ≤ i ≤ m, 1 ≤ j ≤ n is an mxn matrix
B = {bij} where 1 ≤ i ≤ m, 1 ≤ j ≤ n is an mxn matrix
and C = {cij} = A + B,
then C is an mxn matrix and cij = aij + bij for all 1 ≤ i ≤ m, 1 ≤ j ≤ n
What else can I help you with?
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.
What makes two matrices equal?
two matrices are normally considered equal only if they are identical. In other words, every element in the matrix must be equal to the corresponding element in the other matrix.
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 is the condition for the addition of matrices?
The matrices must have the same dimensions.
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.
Write an algorithm for multiplication of two sparse matrices?
how to multiply two sparse matrices
How do you add fractions in matrices?
The usual rules of addition of fractions apply.
What is performing addition subtraction and scalar multiplication of matrices?
Matrix arithmetic
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.
These matrices represent the coordinates of two figures in the plane. Is the product of these matrices defined Answer yes or no?
no
What is commuting use?
Commuting in algebra is often used for matrices. Say you have two matrices, A and B. These two matrices are commutative if A * B = B * A. This rule can also be used in regular binary operations(addition and multiplication). For example, if you have an X and Y. These two numbers would be commutative if X + Y = Y + X. The case is the same for X * Y = Y * X. There are operations like subtraction and division that are not commutative. These are referred to as noncommutative operations. Hope this helps!!
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.
Are matrices associative?
Yes, matrices are associative with respect to addition and multiplication. This means that for any matrices A, B, and C of compatible dimensions, the equations ( (A + B) + C = A + (B + C) ) and ( (AB)C = A(BC) ) hold true. Associativity is a fundamental property that allows for the regrouping of matrices during operations without changing the result.
Why are matrices used for representation while programming?
Let me correct you: two-dimensional arrays are used in programming to represent matrices. (Matrices are objects of mathematics, arrays are objects of programming.)
