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AHSME 1950- part 3

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July 20, 2008
linear algebramatrix

Problem Statement

If the expression (acdb) \begin{pmatrix}a & c \\ d & b \end{pmatrix} has the value ab\minus{}cd for all values of a,b,ca, b, c and dd, then the equation (2x1xx)=3 \begin{pmatrix}2x & 1 \\ x & x \end{pmatrix} = 3:
<spanclass=′latex−bold′>(A)</span> Is satisfied for only 1 value of x<spanclass=′latex−bold′>(B)</span> Is satisified for only 2 values of x<spanclass=′latex−bold′>(C)</span> Is satisified for no values of x<spanclass=′latex−bold′>(D)</span> Is satisfied for an infinite number of values of x<spanclass=′latex−bold′>(E)</span> None of these.<span class='latex-bold'>(A)</span>\ \text{Is satisfied for only 1 value of }x \qquad\\ <span class='latex-bold'>(B)</span>\ \text{Is satisified for only 2 values of }x \qquad\\ <span class='latex-bold'>(C)</span>\ \text{Is satisified for no values of }x \qquad\\ <span class='latex-bold'>(D)</span>\ \text{Is satisfied for an infinite number of values of }x \qquad\\ <span class='latex-bold'>(E)</span>\ \text{None of these.}
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