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Chapter 3: Q8P (page 95)
Show that if, in using the Laplace development, you accidentally multiply the elements of one row by the cofactors of another row, you get zero. Hint: Consider Fact 2b
It has been proved that zero is obtained.
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For each of the following problems write and row reduce the augmented matrix to find out whether the given set of equations has exactly one solution, no solutions, or an infinite set of solutions. Check your results by computer. Warning hint:Be sure your equations are written in standard form. Comment: Remember that the point of doing these problems is not just to get an answer (which your computer will give you), but to become familiar with the terminology, ideas, and notation we are using.
3.
Write each of the items in the second column of (9.2)in index notation.
Find the Eigen values and Eigen vectors of the following matrices. Do some problems by hand to be sure you understand what the process means. Then check your results by computer.
Show that a real Hermitian matrix is symmetric. Show that a real unitary matrix is orthogonal. Note: Thus, we see that Hermitian is the complex analogue of symmetric, and unitary is the complex analogue of orthogonal. (See Section 11.)
Find the symmetric equations and the parametric equations of a line, and/or the equation of the plane satisfying the following given conditions.
Line through and parallel to the line
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