How do you know if a matrix multiplication is possible?
You can only multiply two matrices if their dimensions are compatible , which means the number of columns in the first matrix is the same as the number of rows in the second matrix. If A=[aij] is an m×n matrix and B=[bij] is an n×p matrix, the product AB is an m×p matrix.
What happens when you multiply a matrix by its determinant?
If we multiply a scalar to a matrix A, then the value of the determinant will change by a factor ! This makes sense, since we are free to choose by which row or column we will expand the determinant. Since we can choose this particular row as the one we expand the determinant by the result will become zero!
What is the matrix multiplication rule?
For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix.
What are the rules of determinants?
The determinants will be equivalent to zero if each term of rows and columns are zero. If each term of rows or columns is similar to the column of some other row (or column) then the determinant is equivalent to zero. The interchanging of any two rows (or columns) of the determinant changes its signs.
How do you multiply determinants?
The two determinants to be multiplied must be of the same order. To get the term Tpq (the term in the pth row and the qth column) in teh product, take the pth row of the 1st determinant and multiply by the corresponding terms of the 1th column of the 2nd determinant and add.
Which matrix multiplication is not possible?
So the answer to your question is, a matrix cannot be multiplied by a matrix with a different number of rows then the first has columns.
Does Det AB )= det A )+ det B?
If A and B are n × n matrices, then det(AB) = (detA)(detB). In other words, the determinant of a product of two matrices is just the product of the deter- minants.
Why is matrix multiplication?
The numbers in a matrix can represent data, and they can also represent mathematical equations. In many time-sensitive engineering applications, multiplying matrices can give quick but good approximations of much more complicated calculations.
What is the determinant formula?
The determinant is: |A| = a (ei − fh) − b (di − fg) + c (dh − eg). The determinant of A equals ‘a times e x i minus f x h minus b times d x i minus f x g plus c times d x h minus e x g’. It may look complicated, but if you carefully observe the pattern its really easy!
Can you multiply two determinants?
Two determinants can be multiplied together only if they are of same order. The rule of multiplication is as under: Take the first row of determinant and multiply it successively with 1st, 2nd & 3rd rows of other determinant. The three expressions thus obtained will be elements of 1st row of resultant determinant.