operations with matrices quick check

Answer 1

1. What is matrix addition?
Matrix addition involves adding corresponding elements in two matrices of the same size. For example, if we have matrices A and B of size 2x2:

A = [ 1 2 ]
[ 3 4 ]

B = [ 5 6 ]
[ 7 8 ]

The sum of matrices A and B would be:

A + B = [ 1+5 2+6 ]
[ 3+7 4+8 ]

= [ 6 8 ]
[ 10 12 ]

2. What is matrix multiplication?
Matrix multiplication involves multiplying the elements of rows of the first matrix by the elements of the columns of the second matrix. For example, if we have matrices A and B of size 2x2:

A = [ 1 2 ]
[ 3 4 ]

B = [ 5 6 ]
[ 7 8 ]

The product of matrices A and B would be:

A * B = [ 1*5+2*7 1*6+2*8 ]
[ 3*5+4*7 3*6+4*8 ]

= [ 19 22 ]
[ 43 50 ]

3. What is the identity matrix?
The identity matrix is a square matrix with ones on the diagonal from the top left to the bottom right, and zeros elsewhere. It is denoted by I. For example, the 2x2 identity matrix is:

I = [ 1 0 ]
[ 0 1 ]

The identity matrix acts as the multiplicative identity element for matrices, similar to how the number 1 acts as the multiplicative identity element for regular numbers.