0
2 times 2 equals 4
* * * * *
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Matrix A =
(a b)
(c d)
Matrix B =
(w x)
(y z)
Then AB =
(aw+by ax+bz)
(bw+dy bx+dz)
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∙ 12y ago
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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.
Write an algorithm for multiplication of two sparse matrices?
how to multiply two sparse matrices
Multiplication of two 2 X 2 matrices is?
Closed . . . .A+
Program to display multiplication of two matrix?
The matrix multiplication in c language : c program is used to multiply matrices with two dimensional array. This program multiplies two matrices which will be entered by the user.
Order of operations 15-2x2?
Order of operations--Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. 15-2x2 (fifteen minus two times two) 15-4 11
Multiplication of 2x2 matrices is commutative?
No. Multiplication of matrices is, in general, non-commutative, due to the way multiplication is defined.
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.
Write an algorithm for multiplication of two sparse matrices?
how to multiply two sparse matrices
What is the Flowchart for multiplication of two matrices?
[object Object]
Multiplication of two 2 X 2 matrices is?
Closed . . . .A+
Program to display multiplication of two matrix?
The matrix multiplication in c language : c program is used to multiply matrices with two dimensional array. This program multiplies two matrices which will be entered by the user.
Which operatoins are not commutative?
Subtraction, division, cross multiplication of vectors, multiplication of matrices, etc.
Multiplication of 2 X 2 matrices is commutative?
Sometimes . . A+
Multiplication of 2 X 2 matrices is ______ associative?
always
Order of operations 15-2x2?
Order of operations--Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. 15-2x2 (fifteen minus two times two) 15-4 11
How do you describe a product matrix without multiplying?
You can indicate the multiplication with a multiplication sign. If your matrices are "A" and "B", the product is: A x B In other words, you are indicating the product, but not actually carrying out any multiplication. Anybody who understands about matrices should know what this refers to.
What is performing addition subtraction and scalar multiplication of matrices?
Matrix arithmetic
