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salman213
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3. a) Assume that A^−1 =
1 0 1
2 1 3
1 0 2
Determine the matrix A^TA
1 0 1
2 1 3
1 0 2
Determine the matrix A^TA
A^TA represents the transpose of matrix A multiplied by matrix A. This operation is also known as the inner product or dot product of two matrices.
To determine A^TA, you need to first transpose matrix A by switching the rows and columns. Then, multiply the transposed matrix by matrix A using the rules of matrix multiplication.
Determining A^TA can be useful in various applications such as solving linear equations, finding eigenvectors and eigenvalues, and performing data analysis. It can also help in simplifying calculations and reducing the size of matrices.
Some of the properties of A^TA include: it is a symmetric matrix, its diagonal elements are the squared norms of the columns of A, and its eigenvalues are the squared singular values of A.
No, A^TA can only be determined if A is a square matrix. This is because the transpose of a non-square matrix and the matrix itself have different dimensions and cannot be multiplied together.