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Home Question Bank Math Algebra Archive 2024 December 07

Algebra Questions from Dec 07,2024

Browse the Algebra Q&A Archive for Dec 07,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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1. Resuelve la siguiente operación usando m.c.m. y simplificando al máximo la expresión: \[ \frac{\frac{15}{2} \div \frac{9}{12}-\left(\frac{4 n^{\prime \prime} n^{2}}{3}\right)^{2}}{\frac{5}{1^{\prime \prime} n^{\prime \prime}} \div \frac{3}{6}} \] Suppose the characteristic equation for a matrix \( A \) is given by \( \lambda^{3}+3 \lambda^{2}-9 \lambda-27=0 \). Find the eigenvalues of the matrix \( A \) and give the algebraic multiplicity of each eigenvalue. Eigenvalue: \( \lambda=3 \quad \) Eigenvalue: \( \lambda=\square \) Algebraic multiplicity: Ex: 5 Algebraic multiplicity: \( \quad \hat{v} \) Find the eigenvalues of the matrix \( A=\left[\begin{array}{cccc}4 & 1 & -3 & 2 \\ 0 & 4 & 3 & 3 \\ 0 & 0 & 9 & 1 \\ 0 & 0 & 0 & 4\end{array}\right] \). Give the algebraic multiplicity of each eigenvalue. Eigenvalue: \( \lambda=4 \) Algebraic multiplicity: Ex: \( 5 \quad \hat{m} \) Use your graphing calculator to find the zeros of each quadratic function. Please round to the nearest hundredth if necessary If there is more than one solution, please separate solutions with a comma. If there is no solution, please type "no solution." \[ f(x)=x^{2}-7 x+8 \] 4. \( \quad \) 5. \( f(x)=2 x^{2}+5 x+7 \) 20. \( \left\{\begin{array}{l}-4 m+3 n-6=0 \\ n=\frac{-1}{3} m-8\end{array}\right. \) Solve the system in terms of the arbitrary variable \( x \). \( \begin{array}{r}x-4 y+9 z=9 \\ 2 x-y+2 z=6\end{array} \) The solution set is \( \{(\square, \square)\} \). (Type an expression using \( x \) as the variable.) Solve the system in terms of the arbitrary variable \( x \). \[ \begin{array}{r}5 x-3 y+z=9 \\ \qquad+y=16\end{array} \] The solution set is \( \{(\square, \square, \square)\} \). (Type an expression using \( x \) as the variable.) Find the spectrum of the matrix \( A=\left[\begin{array}{cc}5 & -2 \\ 1 & 2\end{array}\right] \) \( \lambda(A)=\{\hat{E x:} 5 \hat{\imath}, \square \hat{v}\} \) \( \begin{array}{l}\text { Enter the answers in descending } \\ \text { order. }\end{array} \) Part 8 of 8 (h) Given the trinomial \( y^{2}+14 y+49 \), the coefficient of the linear term is \( \square \). Find the \( 8^{\text {th }} \) term of the sequence in a G.P whose \( 3^{\text {rd }} \) term is 1 and \( 11^{\text {th }} \) term is \( \frac{1}{256} \).
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