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What must be true in order to add matrices?
They must have the same dimensions.
Can a matrix of 4x5 be added with a matrix with dimensions of 5x3?
No. You can only add matrices of the same size.
Can a matrix with a dimensions of 2x4 be added to another matrix with dimensions of 2x4?
Yes. In general, two matrices of the same size can be added.
Are parallelograms similar?
No,they are not similar
Addition of two matrices?
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
Do similar matrices have the same eigenvalues?
Yes, similar matrices have the same eigenvalues.
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 the condition for the addition of matrices?
The matrices must have the same dimensions.
Can matrices of the same dimension be multiplied?
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.
How can you use ratios of adjacent sides to prove if two rectangles are similar?
You can use ratios of adjacent sides to prove if two rectangles are similar by comparing to see if the ratios are the same
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.
What are the two conditions that need to be true to prove that two polygons are similar?
That the sides are of the same ratio and that the interior angles are the same.
What must be true in order to add matrices?
They must have the same dimensions.
How does transformations prove that two triangles are similar?
By enlargement on the Cartesian plane and that their 3 interior angles will remain the same
How can you tell whether two matrices can be added?
If both matrices have the same number of columns and rows ex: {1 2 3 4} can not be added with {5 4} b/c they dont have the same amount of numbers
How can I prove that similar matrices have same eigenvalues?
First, we'll start with the definition of an eigenvalue. Let v be a non-zero vector and A be a linear transformation acting on v. k is an eigenvalue of the linear transformation A if the following equation is satisfied:Av = kvMeaning the linear transformation has just scaled the vector, v, not changed its direction, by the value, k.By definition, two matrices, A and B, are similar if B = TAT-1, where T is the change of basis matrix.Let w be some vector that has had its base changed via Tv.Therefore v = T-1wWe want to show that Bw = kvBw = TAT-1w = TAv = Tkv = kTv= kwQ.E.D.
How do you prove that two triangles are similar?
You either show that the corresponding angles are equal or that the lengths of corresponding sides are in the same ratio.
