Define a linear transformation $T:\mathbb{R}^3\rightarrow \mathbb{R}^4$ as $T(1,0,0)=(0,0,0,0), T(0,1,0)=(1,2,3,4), T(0,0,1)=(0,0,0,0)$. Find the matrix of $T$ with respect to the standard bases. That is one possible matrix for $A$.Yankel said:Hello
I have a question, I need to tell if there exist A such as:
[tex]A\cdot \begin{pmatrix} 0\\ 1\\ 4 \end{pmatrix} =\begin{pmatrix} 1\\ 2\\ 3\\ 4 \end{pmatrix}[/tex]
how do you approach this kind of questions ?
thanks !
Matrix multiplication is a mathematical operation that involves multiplying two matrices together to produce a third matrix.
Matrix multiplication is different from regular multiplication in that it involves multiplying individual elements of two matrices to generate a new matrix, whereas regular multiplication involves multiplying two numbers together to produce a single number.
No, a solution is not always possible for matrix multiplication. In order for matrix multiplication to be possible, the number of columns in the first matrix must be equal to the number of rows in the second matrix.
The solution for matrix multiplication is calculated by multiplying the elements in each row of the first matrix by the corresponding elements in each column of the second matrix, and then adding the products together to get the value of each element in the resulting matrix.
Matrix multiplication is used in many fields, including computer graphics, engineering, and economics. It is also used in machine learning and data analysis to perform operations on large datasets.