Determine if the columns of the matrix span R4 [72−58−5−34−9610−27−79215]

We will first enter the matrix A using the comand A=[7,2−5,8;−5,−,4,−9;−7,9,2,15] Use rref(A) reduce matrix to reduced row echelon, we get [10−0.63640.545501−0.27272.09090000] From Theorem the columns of A span Rm if A has a pivot columns of A span Rm. Here, A has not a pivot of position in ebery row. Hence the columns of A not span Rm Result: Not span R4

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BenoguigoliB

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2021-10-15

Determine if the columns of the matrix span $R^{4}$
$[\begin{matrix} 7 & 2 & - 5 & 8 \\ - 5 & - 3 & 4 & - 9 \\ 6 & 10 & - 2 & 7 \\ - 7 & 9 & 2 & 15 \end{matrix}]$

Answer & Explanation

Macsen Nixon

Skilled2021-10-16Added 117 answers

We will first enter the matrix A using the comand
$A = [\begin{matrix} 7, 2 - 5, 8; - 5, -, 4, - 9; - 7, 9, 2, 15 \end{matrix}]$
Use rref(A) reduce matrix to reduced row echelon, we get
$[\begin{matrix} 1 & 0 & - 0.6364 & 0.5455 \\ 0 & 1 & - 0.2727 & 2.0909 \\ 0 & 0 & 0 & 0 \end{matrix}]$
From Theorem the columns of A span $R^{m}$ if A has a pivot columns of A span $R^{m}$ . Here, A has not a pivot of position in ebery row. Hence the columns of A not span $R^{m}$
Result: Not span $R^{4}$

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