# Recent questions tagged matrix

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Show that the matrix $M$ and $M^{T}$ have the same singular values.
Show that the matrix $M$ and $M^{T}$ have the same singular values.Show that the matrix $M$ and $M^{T}$ have the same singular values. ...
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$5(z+1)=3(z+2)+11$ Solve for $z$
$5(z+1)=3(z+2)+11$ Solve for $z$$5(z+1)=3(z+2)+11 Solve for z ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Solve the equation 3n+2=17 1 answer 66 views Solve the equation 3n+2=17Solve the equation 3n+2=17 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Solve the simultaneous equations: \frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2 and \frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1 1 answer 60 views Solve the simultaneous equations: \frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2 and \frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1Solve the simultaneous equations: \frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2 and \frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Solve 3(x-5)=15 1 answer 54 views Solve 3(x-5)=15Solve 3(x-5)=15 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Solve the simultaneous equation 4.9 x+1.5 y=38.3 and 2.7 x-8.6 y=17.8 1 answer 48 views Solve the simultaneous equation 4.9 x+1.5 y=38.3 and 2.7 x-8.6 y=17.8Solve the simultaneous equation 4.9 x+1.5 y=38.3 and 2.7 x-8.6 y=17.8 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Solve the simultaneous equations 3x+y=8 and x+2 y=6 1 answer 83 views Solve the simultaneous equations 3x+y=8 and x+2 y=6Solve the simultaneous equations 3x+y=8 and x+2 y=6 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Solve for x: 3.5^{x}=0,6 1 answer 36 views Solve for x: 3.5^{x}=0,6Solve for x: 3.5^{x}=0,6 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Solve the simultaneous equations: 3 x-y+z=5; 2 x+2 y+3 z=4 and x+3 y-z=11 1 answer 59 views Solve the simultaneous equations: 3 x-y+z=5; 2 x+2 y+3 z=4 and x+3 y-z=11Solve the simultaneous equations: 3 x-y+z=5; 2 x+2 y+3 z=4 &nbsp;and x+3 y-z=11 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Given the following simultaneous equations: x+3 y=-1 and -3 x+6 y=8, solve the given simultaneous equations by the substitution method. 1 answer 108 views Given the following simultaneous equations: x+3 y=-1 and -3 x+6 y=8, solve the given simultaneous equations by the substitution method.Given the following simultaneous equations: x+3 y=-1 and -3 x+6 y=8, solve the given simultaneous equations by the substitution method. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Given the simultaneous equations 7 x-3 y=41 and 3 x-y=17, solve for x and y by matrix method. 1 answer 57 views Given the simultaneous equations 7 x-3 y=41 and 3 x-y=17, solve for x and y by matrix method.Given the simultaneous equations 7 x-3 y=41 and &nbsp;3 x-y=17, solve for x and y by matrix method. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine the VanderMonde matrix for the points \left[0, \frac{1}{9}, \frac{2}{9}, \ldots, 1\right]. 0 answers 35 views Determine the VanderMonde matrix for the points \left[0, \frac{1}{9}, \frac{2}{9}, \ldots, 1\right].Determine the VanderMonde matrix for the points \left0, \frac{1}{9}, \frac{2}{9}, \ldots, 1\right. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 To find eigenvalues one uses a QR algorithm involving successive iterations of Givens rotations. Apply one complete iteration of Givens rotations to this matrix. 1 answer 55 views To find eigenvalues one uses a QR algorithm involving successive iterations of Givens rotations. Apply one complete iteration of Givens rotations to this matrix.Consider the tri-diagonal matrix$$ \mathbf{A}=\left(\begin{array}{lll} 4 &amp; 2 &amp; 0 \\ 2 &amp; 2 &amp; 1 \\ 0 &amp; 1 &amp; 1 \end{array}\right) ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If the eigenvalues of$\mathbf{A}$are$100,-50,3 \pm 5 \sqrt{-1}$, then find a lower bound on cond$(\mathbf{A})$1 answer 54 views If the eigenvalues of$\mathbf{A}$are$100,-50,3 \pm 5 \sqrt{-1}$, then find a lower bound on cond$(\mathbf{A})$Given a nonsingular$n \times n$matrix$\mathbf{A}$, and$n \times 1$vectors$\mathbf{x}, \hat{\mathbf{x}}, \mathbf{b}=\mathbf{A x}$, and$\hat{\mat ...
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Find a better bound for $$\frac{\|\mathbf{x}-\hat{\mathbf{x}}\|}{\|\mathbf{x}\|} \times \frac{\|\mathbf{b}\|}{\|\mathbf{b}-\hat{\mathbf{b}}\|}$$
Find a better bound for $$\frac{\|\mathbf{x}-\hat{\mathbf{x}}\|}{\|\mathbf{x}\|} \times \frac{\|\mathbf{b}\|}{\|\mathbf{b}-\hat{\mathbf{b}}\|}$$Given a nonsingular $n \times n$ matrix $\mathbf{A}$, and $n \times 1$ vectors $\mathbf{x}, \hat{\mathbf{x}}, \mathbf{b}=\mathbf{A x}$, and $\hat{\mat ... close 1 answer 63 views Prove that for$\mathbf{A} \in \mathbb{R}^{m \times n}$,$\mathbf{A}^{\top} \mathbf{A}$is positive semi-definite. If$\operatorname{null}(\mathbf{A})=\{0\}$, then$\mathbf{A}^{\top} \mathbf{A}$is positive definite.Prove that for &nbsp;$\mathbf{A} \in \mathbb{R}^{m \times n}$,$\mathbf{A}^{\top} \mathbf{A}$is positive semi-definite. If$\operatorname{null}(\math ...
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Prove that a symmetric matrix is positive semi-definite if and only if all of its eigenvalues are nonnegative, and positive definite if and only if all of its eigenvalues are positive.Prove that a symmetric matrix is positive semi-definite if and only if all of its eigenvalues are nonnegative, and positive definite if and only if al ...
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A symmetric matrix A is positive semi-definite if
A symmetric matrix A is positive semi-definite ifA symmetric matrix A is positive semi-definite if ...
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A matrix $\mathbf{A} \in \mathbb{R}^{n \times n}$ is said to be symmetric if
A matrix $\mathbf{A} \in \mathbb{R}^{n \times n}$ is said to be symmetric ifA matrix $\mathbf{A} \in \mathbb{R}^{n \times n}$ is said to be symmetric if ...
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A matrix $\mathbf{Q} \in \mathbb{R}^{n \times n}$ is said to be orthogonal if
A matrix $\mathbf{Q} \in \mathbb{R}^{n \times n}$ is said to be orthogonal ifA matrix $\mathbf{Q} \in \mathbb{R}^{n \times n}$ is said to be orthogonal if ...
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The determinant of a square matrix can be defined as ...
The determinant of a square matrix can be defined as ...The determinant of a square matrix can be defined as ... ...
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The trace of a square matrix is ...
The trace of a square matrix is ...The trace of a square matrix is ... ...
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We say that a nonzero vector $\mathrm{x} \in \mathbb{R}^{n}$ is an eigenvector of A corresponding to eigenvalue $\lambda$ if
We say that a nonzero vector $\mathrm{x} \in \mathbb{R}^{n}$ is an eigenvector of A corresponding to eigenvalue $\lambda$ ifFor a square matrix $\mathbf{A} \in \mathbb{R}^{n \times n}$, there may be vectors which, when $\mathbf{A}$ is applied to them, are simply scaled by s ...
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Find values of $x$ for which $A B$ is a singular matrix.
Find values of $x$ for which $A B$ is a singular matrix.(a) Given that $A=$ $$\left(\begin{array}{cc} 3 &amp; x \\ x+1 &amp; 2 \end{array}\right)$$ and $B=$  \left(\begin{array}{ll} 1 &amp; 2 \\ 3 &amp; ...