- #1
ajayguhan
- 153
- 1
Homework Statement
A=[1 0 0]
[1 0 1]
[0 1 0]
Find A^50
Homework Equations
The Attempt at a Solution
I'm sure that we can't multiply it 50 times...it's a tedious process , there must be a short cut
ajayguhan said:Homework Statement
A=[1 0 0]
[1 0 1]
[0 1 0]
Find A^50
Homework Equations
The Attempt at a Solution
I'm sure that we can't multiply it 50 times...it's a tedious process , there must be a short cut
Another way to write ##A^{50}## is ##(A^2)^{25}##. What's ##A^2## ? ##A^4 = (A^2)^2## ? ##A^6 = (A^2)^3## ? Do you see a pattern emerging? Can you prove that this pattern is valid for all ##A^{2n}=(A^2)^n## ?ajayguhan said:I'm sure that we can't multiply it 50 times...it's a tedious process , there must be a short cut
Matrix multiplication is a mathematical operation that involves multiplying two matrices to create a new matrix. It is denoted by the symbol "x" or by placing the matrices side by side.
There are two main rules for matrix multiplication: 1) the number of columns in the first matrix must be equal to the number of rows in the second matrix, and 2) the resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.
To perform matrix multiplication, you multiply each element in a row of the first matrix by the corresponding element in a column of the second matrix, and then add the products together to get the element in the resulting matrix. This process is repeated for each element in the resulting matrix.
Matrix multiplication is used in various fields of science and engineering to solve complex problems involving multiple variables. It is also used in computer graphics and machine learning algorithms, as well as in solving systems of linear equations.
Yes, there are a few special properties of matrix multiplication. The commutative property does not apply, which means that the order of the matrices matters. The associative property does apply, which means that the grouping of matrices can be changed without affecting the result. Finally, the identity property applies, which means that multiplying a matrix by the identity matrix will result in the original matrix.