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If A is a 3x4 matrix with values ([a11, a12, a13, a14], [a21, a22, a23, a24], [a31, a32, a33, a34]) then its transpose AT is a 4x3 matrix values with its values changed diagonally like so, ([a11, a21, a31], [a12, a22, a32], [a13, a23, a33], [a14, a24, a34])
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What will be the dimensions of the new matrix formed by multiplying a 3 X 4 matrix and a 4 X 1 matrix?
3x1 matrix
Can a 3 x 2 matrix be added or subtracted with a 4 x 3 matrix?
No.Two matrices A and B can be added or subtracted if and only if they have the same number of rows and columns. That is a 3 x 2 matrix can be added or subtracted only with another 3 x 2 matrix.
Can a matrix with dimensions of 4 X 5 be added to another matrix with dimensions of 5 X 3?
No. Matrix addition (or subtraction) is defined only for matrices of the same dimensions.
What will be the dimensions of the new matrix formed by multiplying a 2 by 4 matrix and a 4 by 5 matrix?
2 x 5 matrix
Is eigenvalue applicable only to n x n matrices?
The answer is yes, and here's why: Remember that for the eigenvalues (k) and eigenvectors (v) of a matrix (M) the following holds: M.v = k*v, where "." denotes matrix multiplication. This operation is only defined if the number of columns in the first matrix is equal to the number of rows in the second, and the resulting matrix/vector will have as many rows as the first matrix, and as many columns as the second matrix. For example, if you have a 3 x 2 matrix and multiply with a 2 x 4 matrix, the result will be a 3 x 4 matrix. Applying this to the eigenvalue problem, where the second matrix is a vector, we see that if the matrix M is m x n and the vector is n x 1, the result will be an m x 1 vector. Clearly, this can never be a scalar multiple of the original vector.
What will be the dimensions of the new matrix formed by multiplying a 3 X 4 matrix and a 4 X 1 matrix?
3x1 matrix
Can a 3 x 2 matrix be added or subtracted with a 4 x 3 matrix?
No.Two matrices A and B can be added or subtracted if and only if they have the same number of rows and columns. That is a 3 x 2 matrix can be added or subtracted only with another 3 x 2 matrix.
What will be the dimensions of a new matrix formed by multiplying a 2 X 4 matrix and a 4 X 5 matrix?
It will be a 2 x 5 matrix.
Can a matrix with dimensions of 4 X 5 be added to another matrix with dimensions of 5 X 3?
No. Matrix addition (or subtraction) is defined only for matrices of the same dimensions.
What is a 9 cell matrix?
3 x 3 matrix
Can a matrix with dimensions of 2 X 4 be added to another matrix that has dimensions of 2 X 4?
no
What are squares with numbers in them in text?
A rectangle containing numbers are called "matrix" (1 0 0 1) (3 4 8 0) is a 2 x 4 matrix a SQUARE containing numbers is a n x n matrix, or square matrix (1 0) (5 6) is a square matrix (1) is a square matrix
Can a matrix with dimensions of 2 X 4 be added to another matrix with dimensions of 2 X 4?
Yes.
What will be the dimensions of the new matrix formed by multiplying a 2 by 4 matrix and a 4 by 5 matrix?
2 x 5 matrix
What is 2 x 4 matrix?
A 2x4 matrix has 2 rows (horizontal) and 4 columns (vertical). Ex: [1 2 3 4] [5 6 7 8]
Which type of matrix can be multiplied to another matrix and result in that matrix?
That is called the identity matrix. For example, (3,1,4)t x (1,1,1) = (3,1,4)t In this case (1,1,1) is the identity matrix. Another example is 5 11 1 0 1 11 x = 4 3 0 1 4 3 (You will have to imagine the brackets around the matrices as I did not know how to draw them in.) In this case 1 0 is the identity matrix. 0 1
Is eigenvalue applicable only to n x n matrices?
The answer is yes, and here's why: Remember that for the eigenvalues (k) and eigenvectors (v) of a matrix (M) the following holds: M.v = k*v, where "." denotes matrix multiplication. This operation is only defined if the number of columns in the first matrix is equal to the number of rows in the second, and the resulting matrix/vector will have as many rows as the first matrix, and as many columns as the second matrix. For example, if you have a 3 x 2 matrix and multiply with a 2 x 4 matrix, the result will be a 3 x 4 matrix. Applying this to the eigenvalue problem, where the second matrix is a vector, we see that if the matrix M is m x n and the vector is n x 1, the result will be an m x 1 vector. Clearly, this can never be a scalar multiple of the original vector.
