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Unformatted text preview: voltage V ) and one current source (with current I ). Solve the circuit with these symbolic values for the sources. Determine the 2 2 fundamental matrix F of the problem. That is, the matrix such that E J = F V I where E is the voltage across the current source and J is the current through the voltage source. 3. Consider the matrix A = 1 1 2 1 1 3 1 2 7 (a) Calculate the determinant of A (because the determinant of A is not zero, we know it is invertible). (b) Calculate the inverse of A . 4. Suppose A and B are invertible, square matrices. Give an example to show that A + B is not necessarily invertible. 5. Let T be the linear transformation from R 5 R 5 which sends a vector x = ( x 1 ,x 2 ,x 3 ,x 4 ,x 5 ) to the vector T ( x ) = ( x 1 + x 2 ,x 2 + x 3 ,x 3 + x 4 ,x 4 + x 5 ,x 5 + x 1 ). (a) Write the matrix A that corresponds to T . (b) Is A is invertible? Justify briey....
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- Spring '08