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Chapter 1: Q13 (page 39)
Question: If A is a non-zero matrix of the form, then the rank of A must be 2.
Answer:
True, If A is a non-zero matrix of the form, then the rank of A is 2.
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Solve each system in Exercises 1–4 by using elementary row operations on the equations or on the augmented matrix. Follow the systematic elimination procedure.
If Ais a matrix with eigenvalues 3 and 4 and if localid="1668109698541" is a unit eigenvector of A, then the length of vector Alocalid="1668109419151" cannot exceed 4.
In Exercises 9, write a vector equation that is equivalent to
the given system of equations.
9. \({x_2} + 5{x_3} = 0\)
\(\begin{array}{c}4{x_1} + 6{x_2} - {x_3} = 0\\ - {x_1} + 3{x_2} - 8{x_3} = 0\end{array}\)
Write the vector \(\left( {\begin{array}{*{20}{c}}5\\6\end{array}} \right)\) as the sum of two vectors, one on the line \(\left\{ {\left( {x,y} \right):y = {\bf{2}}x} \right\}\) and one on the line \(\left\{ {\left( {x,y} \right):y = x/{\bf{2}}} \right\}\).
In Exercise 2, compute \(u + v\) and \(u - 2v\).
2. \(u = \left[ {\begin{array}{*{20}{c}}3\\2\end{array}} \right]\), \(v = \left[ {\begin{array}{*{20}{c}}2\\{ - 1}\end{array}} \right]\).
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