Linear Algebra - 4 Edition - Chapter 5.1 - Problem 11
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# A scalar matrix is a square matrix of the form XI for some scalar A; that is, a scalar

Linear Algebra | 4th Edition

Problem 11

A scalar matrix is a square matrix of the form XI for some scalar A; that is, a scalar matrix is a diagonal matrix in which all the diagonal entries are equal. (a) Prove that if a square matrix A is similar to a scalar matrix XI, then A- XL (b) Show that a diagonalizable matrix having only one eigenvalue is a scalar matrix.

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Introduction to Vectors Part 1 Saadiq Shaik September 2016 1 Cartesian Coordinates in Space A vector is de▯ned as a quantity with both a magnitude and direction. We will be dealing with vectors in three dimensional space, so familiarize yourself with the three dimensional coordinate system. The coordinate planes are the xy-plane, yz-plane, and xz-plane. There are eight octants, but the one we will be dealing with most is the ▯rst octant, which contains positive x, y, and z values. Imagine a point P with the coordinates (a ;b ;c ) and a point Q with 1 1 1 the coordinates 2a2;b3;c ) in three dimensional space. The distance between them is given by the distance formu

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