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Chapter 8: Problem 64
Evaluate the determinant, in which the entries are functions. Determinants of this type occur when changes of variables are made in calculus. $$\left|\begin{array}{cc} 3 x^{2} & -3 y^{2} \\ 1 & 1 \end{array}\right|$$
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Use the matrix capabilities of a graphing utility to write the matrix in reduced row-echelon form . Use the matrix capabilities of a graphing utility to write the matrix in reduced row-echelon form. $$\left[\begin{array}{rrrr} -4 & 1 & 0 & 6 \\ 1 & -2 & 3 & -4 \end{array}\right]$$
Find the point of equilibrium of the demand and supply equations. The point of equilibrium is the price \(p\) and the number of units \(x\) that satisfy both the demand and supply equations. Demand \(\quad\) Supply \(p=400-0.0002 x \quad p=225+0.0005 x\)
Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form. $$\left[\begin{array}{lllr} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & -1 \\ 0 & 0 & 0 & 2 \end{array}\right]$$
Create a system of linear equations in two variables that has the solution (2,-1) as its only solution. (There are many correct answers.)
Determine whether the statement is true or false. Justify your answer. If a system of linear equations has no solution, then the lines must be parallel.
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