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How do you identify the dimensions of a matrix?
To identify the dimensions of a matrix, count the number of rows and columns it contains. The dimensions are expressed as "rows × columns." For example, a matrix with 3 rows and 4 columns is described as a 3×4 matrix.
Can a matrix with dimensions of 2 X 4 be added to another matrix that has dimensions of 2 X 4?
no
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 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.
How can you determine whether a matrix product AB is defined?
To determine whether the matrix product ( AB ) is defined, you need to check the dimensions of the matrices ( A ) and ( B ). Specifically, if matrix ( A ) has dimensions ( m \times n ) and matrix ( B ) has dimensions ( p \times q ), the product ( AB ) is defined if and only if the number of columns in ( A ) (i.e., ( n )) is equal to the number of rows in ( B ) (i.e., ( p )). If this condition is met, the resulting matrix ( AB ) will have dimensions ( m \times q ).
Can a matrix with dimensions of 2 X 4 be added to another matrix with dimensions of 2 X 5?
No. Matrix addition (or subtraction) is defined only for matrices of the same dimensions.
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.
How do you identify the dimensions of a matrix?
To identify the dimensions of a matrix, count the number of rows and columns it contains. The dimensions are expressed as "rows × columns." For example, a matrix with 3 rows and 4 columns is described as a 3×4 matrix.
Can a matrix with dimensions of 2 X 4 be added to another matrix that has dimensions of 2 X 4?
no
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 3 X 4 matrix and a 4 X 1 matrix?
3x1 matrix
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
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.
What are the dimensions of the matrix product?
2*2
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 you add a 1x3 matrix to a 3x2 matrix?
No, you cannot add a 1x3 matrix to a 3x2 matrix because the two matrices have different dimensions. For matrix addition to be valid, both matrices must have the same dimensions. In this case, a 1x3 matrix has one row and three columns, while a 3x2 matrix has three rows and two columns, making them incompatible for addition.
How can you determine whether a matrix product AB is defined?
To determine whether the matrix product ( AB ) is defined, you need to check the dimensions of the matrices ( A ) and ( B ). Specifically, if matrix ( A ) has dimensions ( m \times n ) and matrix ( B ) has dimensions ( p \times q ), the product ( AB ) is defined if and only if the number of columns in ( A ) (i.e., ( n )) is equal to the number of rows in ( B ) (i.e., ( p )). If this condition is met, the resulting matrix ( AB ) will have dimensions ( m \times q ).
