Linear Algebra: Orthogonal ColumnsLet M be
\begin{matrix}
1 & 3 & 1\
2 & -2 & a\
1 & 1 & b
\end{matrix}
and let a and b be such that the columns of M are orthogonat. Compute aPick ONE option−21−1212Clear Selection
Q. Linear Algebra: Orthogonal ColumnsLet M be
\begin{matrix}
1 & 3 & 1\
2 & -2 & a\
1 & 1 & b
\end{matrix}
and let a and b be such that the columns of M are orthogonat. Compute aPick ONE option−21−1212Clear Selection
Write Matrix M: First, let's write down the matrix M with the given elements and the unknowns a and b:M = \left| \begin{array}{ccc}\(\newline1 & 2 & 1 (\newline\)3 & -2 & 1 (\newline\)1 & a & b (\newline\)\end{array} \right|\)For the columns of M to be orthogonal, the dot product of any two distinct columns must be zero. Let's start by taking the dot product of the first and second columns.Dot product of first and second columns:(1)(2)+(3)(−2)+(1)(a)=2−6+a=a−4We want this to be equal to zero for orthogonality:a−4=0
Find Dot Product: Now, let's solve for a:a−4=0a=4We have found the value of a that makes the first and second columns orthogonal.
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