Linear Algebra 1. Given that det(C) = -11, where \[ C = \begin{bmatrix} 1 & 4 & 7 \\ 0 & 3 & 1 \\ 1 & 0 & 2 \end{bmatrix} \],find the determinant of the given matrix.\[ D = \begin{bmatrix} 1 & 10 & 9 \\ 0 & 3 & 1 \\ 1 & 6 & 4 \end{bmatrix} \]\[ E = \begin{bmatrix} 1 & 4 & 7 \\ 0 & 1 & \frac{1}{3} \\ 1 & 0 & 2 \end{bmatrix} \]\[ F = \begin{bmatrix} 1 & 4 & 7 \\ 0 & 3 & 1 \\ 0 & -4 & -5 \end{bmatrix} \]

Given that det(C)=-11 where C=147031102 we have D=1109031164 The determinant of the matrix is given…

Answered: 147 1. Given that det(C) = -11, where C…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Linear Algebra

1. Given that det(C) = -11, where
\[ C = \begin{bmatrix} 1 & 4 & 7 \\ 0 & 3 & 1 \\ 1 & 0 & 2 \end{bmatrix} \],
find the determinant of the given matrix.

\[ D = \begin{bmatrix} 1 & 10 & 9 \\ 0 & 3 & 1 \\ 1 & 6 & 4 \end{bmatrix} \]

\[ E = \begin{bmatrix} 1 & 4 & 7 \\ 0 & 1 & \frac{1}{3} \\ 1 & 0 & 2 \end{bmatrix} \]

\[ F = \begin{bmatrix} 1 & 4 & 7 \\ 0 & 3 & 1 \\ 0 & -4 & -5 \end{bmatrix} \]

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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