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MATRICES
[CHAP. 15
15.87. Find a unit vector which is orthogonal to each of the vectors
15.88. If matrix.
are mutually orthogonal, prove that
is an orthogonal
Can you determine an analogous result for a unitary matrix?
SYSTEMS OF LINEAR EQUATIONS 15.89. Solve the systems of equations
15.90. The currents /i,/2.^s
an
d I* in an electric network satisfy the system of equations
Find Is. 15.91. Classify each of the following systems of equations according as they (i) have a unique solution, (ii) are inconsistent (iii) are dependent. Determine solutions where they exist.
15.92. For what value or values of k will the system of equation
have solutions other than the trivial one? Determine some of these solutions.
15.93. Given the system of equations
show that any two of xlt x&x3 can be
solved in terms of the remaining one and thus that there are infinitely many solutions.
15.94. Given the system of equations can be solved in terms of the remaining one.
determine whether any two of xltx2,xs