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No. The number of columns of the first matrix needs to be the same as the number of rows of the second.
So, matrices can only be multiplied is their dimensions are k*l and l*m. If the matrices are of the same dimension then the number of rows are the same so that k = l, and the number of columns are the same so that l = m. And therefore both matrices are l*l square matrices.
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Do similar matrices have the same eigenvalues?
Yes, similar matrices have the same eigenvalues.
What is the condition for the addition of matrices?
The matrices must have the same dimensions.
Do similar matrices have the same eigenvectors?
No, in general they do not. They have the same eigenvalues but not the same eigenvectors.
What is linear combination in matrices?
If X1, X2 , ... , Xn are matrices of the same dimensions and a1, a2, ... an are constants, then Y = a1*X1 + a2*X2 + ... + an,*Xn is a linear combination of the X matrices.
22 matrix with 33 matrix multiplication?
It is not possible. The number of columns in the first matrix must be the same as the number of rows in the second. That is, matrices, X (kxl) and Y (mxn) can only be multiplied [in that order] if l = m.
Do similar matrices have the same eigenvalues?
Yes, similar matrices have the same eigenvalues.
What is the condition for the addition of matrices?
The matrices must have the same dimensions.
What is order of the resultant matrix AB when two matrices are multiplied and the order of the Matrix A is m n order of Matrix B is n p Also state the condition under which two matrices can be mult?
the order is m p and the matrices can be multiplied if and only if the first one (matrix A) has the same number of columns as the second one (matrix B) has rows i.e)is Matrix A has n columns, then Matrix B MUST have n rows.Equal Matrix: Two matrices A=|Aij| and B=|Bij| are said to be equal (A=B) if and only if they have the same order and each elements of one is equal to the corresponding elements of the other. Such as A=|1 2 3|, B=|1 2 3|. Thus two matrices are equal if and only if one is a duplicate of the other.
If only one dimension of a shape is doubled what is the volume multiplied by?
2
Do similar matrices have the same eigenvectors?
No, in general they do not. They have the same eigenvalues but not the same eigenvectors.
How do you know if two matrices can actually be multiplied?
The number of columns in the first matrix must equal the number of rows in the second.
How can you prove that similar matrices have the same trace?
you tell me
What is linear combination in matrices?
If X1, X2 , ... , Xn are matrices of the same dimensions and a1, a2, ... an are constants, then Y = a1*X1 + a2*X2 + ... + an,*Xn is a linear combination of the X matrices.
22 matrix with 33 matrix multiplication?
It is not possible. The number of columns in the first matrix must be the same as the number of rows in the second. That is, matrices, X (kxl) and Y (mxn) can only be multiplied [in that order] if l = m.
What is dimension of enthalpy?
The dimension of enthalpy is energy per unit mass (J/kg) or energy per unit amount of substance (J/mol). It has the same dimensions as energy, which is measured in joules (J).
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 will be dimension of vector space of all symmetric matrices of order n x n with real entries and trace zero?
(n^2-n)/2-1
