Recent questions tagged coefficient-matrix

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How many real solutions are there to the system of equations?\[y^2 = x^2 + 5x - 27\]\[x + 5 = y^2 \]
447
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Solve the equation \(x^2+2x+1=0\). Use latex code for an WYSIWYG editor
423
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Solve the following system of equations:\[\left[\begin{array}{rrr}1 & 2 & 3 \\-1 & 4 & 2 \\3 & -6 & 0\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3\end{array}\ri...
472
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How do you solve a system of linear equations using substitution?
308
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Solve the system of equations $3x - 2y + z = 1$, $x + y + 2z = 2$, and $2x - y + 3z = 3$ using matrices.
549
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Solve the system of equations $x + 2y + 3z = 1$, $2x + y + z = 2$, and $3x + 2y + 2z = 3$ using matrices.
357
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Solve the system of equations $2x - y = 1$ and $x + 2y = 5$ using matrices.
261
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Solve the system of equations $3x + y = 5$ and $x - y = 1$ using matrices.
355
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Solve the system of equations $2x + 3y = 1$ and $x - 2y = 3$ using matrices.
153
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Solve $\dfrac{x^2 + x - 6}{x^2 - 2x - 3} = 0$
190
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Solve $\frac{x^2 + 2x + 3}{x^2 - 4} = 0$
153
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Solve $\dfrac{2x^2 - 3x + 1}{x^2 + 1} = 0$
394
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Solve $\begin{cases} x - y + 2z = 1 \\ 2x + 3y - z = 2 \\ 3x - 2y + 3z = 3 \end{cases}$
277
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Solve the equations $\begin{cases} 2x + y + 3z = 2 \\ x - 2y + z = 3 \\ 3x + y - 2z = 1 \end{cases}$
361
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Solve $\begin{cases} x + y - z = 0 \\ 2x - y + z = 1 \\ 3x + 2y - 2z = 2 \end{cases}$
309
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Solve the system of equations $\begin{cases} 2x - y + 3z = 1 \\ x + 2y - z = 2 \\ 3x - y + 2z = 3 \end{cases}$
244
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Solve the simultaneous equation $\begin{cases} x + y + z = 3 \\ x - y + 2z = 0 \\ 2x + 3y - z = 1 \end{cases}$
193
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Calculate the value of \(x\) if \(2(3-x)=8\).
198
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Solve the simultaneous equations below:\[\begin{aligned}&3 x-y+z=5 \\&2 x+2 y+3 z=4 \\&x+3 y-z=11\end{aligned}\]
200
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The complex numbers \(z\) and \(w\) satisfy the simultaneous equations\[\begin{aligned}&2 z+\mathrm{i} w=-1 \\&z-w=3+3 \mathrm{i}\end{aligned}\](a) Use algebra to find \(...
203
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Show that \(\log _{2}(\sqrt[3]{5})=\frac{\log _{2} 5}{3}\)
163
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Show that \(\log \left(\frac{10}{100}\right)=\log 10-\log 100\)
238
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Show that \(\log (10 \cdot 100)=\log 10+\log 100\).
249
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If \(\frac{\log x}{y-z}=\frac{\log y}{z-x}=\frac{\log z}{x-y}\) then what is \(x^{x} \cdot y^{y} \cdot z^{z}\)
169
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Find the value of \(x\)\[\log \left(98+\sqrt{x^{2}-12 x+36}\right)=2\]
189
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Find the value of \(x\), if\[\sqrt{8^{0}+\frac{2}{3}}=(0.6)^{2-3 x}\]
524
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Find \(x\) and \(y\), if\[\begin{aligned}&z^{3}=\sqrt{36^{5}}, y=x^{-5} \\&x=\log _{6} z-\frac{2}{3}\end{aligned}\]
369
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Find the solution to the following system.\[\begin{aligned}&x_{1}^{\prime}=x_{1}+2 x_{2} \quad x_{1}(0)=0 \\&x_{2}^{\prime}=3 x_{1}+2 x_{2} \quad x_{2}(0)=-4\end{aligned}...
254
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Convert the following system to matrix form.\[\begin{aligned}&x_{1}^{\prime}=4 x_{1}+7 x_{2} \\&x_{2}^{\prime}=-2 x_{1}-5 x_{2}\end{aligned}\]
262
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Solve the simultaneous equations \begin{aligned} &x^{2}+y^{2}=49 \\ &y^{2}-5 x=49 \end{aligned}
127
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237
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The HCF of \(12 x^{2} y ; 42 x^{3} y^{2} ; 27 x y\) is:
249
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Consider the system of equations\[\begin{aligned}&x+y-z=a \\&x-y+2 z=b .\end{aligned}\]a) Find the general solution of the homogeneous equation, so \(a=b=0\).b) A particu...
316
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Consider the system of linear equations\[\begin{array}{rc}k x+y+z & =1 \\x+k y+z & =1 \\x+y+k z & =1\end{array}\]For what value(s) of \(k\) does this have (i) a unique so...
344
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Consider the system of equations\[\begin{aligned}&x+y-z=a \\&x-y+2 z=b .\end{aligned}\]a) Find the general solution of the homogeneous equation.b) A particular solution o...
453
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Solve the following system of equations.\[\begin{aligned}&x-y=2 \\&x+2 y=11 \\&-2 x+5 y=5\end{aligned}\]
379
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Solve the following system of equations.\[\begin{aligned}&x-3 y=-1 \\&x+y=7 \\&2 x+5 y=20\end{aligned}\]
888
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Solve the following system of equations. Let \(z\) be the parameter.\[\begin{aligned}&x+2 y+3 z=1 \\&2 x+y-z=6\end{aligned}\]
751
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Solve the following system of equations. Let \(z\) be the parameter.\[\begin{aligned}&x+3 y+6 z=19 \\&2 x-3 y+3 z=2\end{aligned}\]
303
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For the following system of equations, tell how many solutions there are in nonnegative integers.\[\begin{array}{r}x+3 y+z=82 \\7 y+2 z=42\end{array}\]
352
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For the following system of equations, tell how many solutions there are that are positive and result in \(z\) being a positive integer.\[\begin{array}{r}x+2 y+z=88 \\7 y...
454
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Solve the system of two equations in two unknowns.\[\begin{aligned}&2 x-3 y=5 \\&8 x-12 y=20\end{aligned}\]
520
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Solve the system of two equations in two unknowns.\[\begin{aligned}&5 x+6 y=1 \\&15 x+18 y=3\end{aligned}\]
632
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Solve the system of two equations in two unknowns.\[\begin{aligned}&y=5 x+2 \\&-10 x+2 y=1\end{aligned}\]
701
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Solve the system of two equations in two unknowns.\[\begin{aligned}&x=1-2 y \\&3 x+6 y=10\end{aligned}\]
824
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Solve the system of equations by the Substitution Method.\[\begin{aligned}&4 x-9 y=-1 \\&3 x+4 y=10\end{aligned}\]
816
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Solve the system of equations by the Substitution Method.\[\begin{aligned}&y=-2 x+3 \\&2 x-5 y=-51\end{aligned}\]
551
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Solve the system of equations by the Substitution Method.\[\begin{aligned}&x=2 y+1 \\&4 x-3 y=14\end{aligned}\]
492
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Solve the system of equations by graphing.\[\begin{aligned}&3 x-y=5 \\&4 x+y=2\end{aligned}\]
520
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Consider a free particle in two dimensions confined by the boundary$$G:=\{(x, y):|x y|=1\} .$$Solve the eigenvalue problem$$\Delta \psi+k^{2} \psi=0$$where$$k^{2}=\frac{2...
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