If the matrix $$A=123024323213687$$αis of rank $$3Then$$ α$$=$$

$$A=123024323213687$$α$$R2-2R1$$ $$R3-3R1$$ $$R4-6R1$$~$$123000-320-4-830-4-11$$α$$R2$$→$$R3$$ $$R4-R3$$~$$12300-4-8300-3200-3$$α$$-3R4-R3$$~$$12300-4-8300-32000$$α$$-5RankA=3$$ ⇒α−$$5=0$$ ⇒α$$=5$$

Elementary row operations (Transformation)

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If the matrix $A = [\begin{matrix} 1 & 2 & 3 & 0 \\ 2 & 4 & 3 & 2 \\ 3 & 2 & 1 & 3 \\ 6 & 8 & 7 & α \end{matrix}]$ is of rank $3$ Then $α =$

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Solution

$A = [\begin{matrix} 1 & 2 & 3 & 0 \\ 2 & 4 & 3 & 2 \\ 3 & 2 & 1 & 3 \\ 6 & 8 & 7 & α \end{matrix}]$
$R_{2} - 2 R_{1} R_{3} - 3 R_{1} R_{4} - 6 R_{1}$ $~ [\begin{matrix} 1 & 2 & 3 & 0 \\ 0 & 0 & - 3 & 2 \\ 0 & - 4 & - 8 & 3 \\ 0 & - 4 & - 11 & α \end{matrix}]$
$R_{2} \to R_{3} R_{4} - R_{3}$ $~ [\begin{matrix} 1 & 2 & 3 & 0 \\ 0 & - 4 & - 8 & 3 \\ 0 & 0 & - 3 & 2 \\ 0 & 0 & - 3 & α - 3 \end{matrix}]$
$R_{4} - R_{3}$ $~ [\begin{matrix} 1 & 2 & 3 & 0 \\ 0 & - 4 & - 8 & 3 \\ 0 & 0 & - 3 & 2 \\ 0 & 0 & 0 & α - 5 \end{matrix}]$
Rank $A = 3 \Rightarrow α - 5 = 0 \Rightarrow α = 5$

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Elementary row operations (Transformation)

Remember concepts with our Masterclasses.

If the matrix A=123024323213687αis of rank 3Then α=

A=123024323213687αR2-2R1 R3-3R1 R4-6R1~123000-320-4-830-4-11αR2→R3 R4-R3~12300-4-8300-3200-3α-3R4-R3~12300-4-8300-32000α-5RankA=3 ⇒α−5=0 ⇒α=5

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If the matrix $A = [\begin{matrix} 1 & 2 & 3 & 0 \\ 2 & 4 & 3 & 2 \\ 3 & 2 & 1 & 3 \\ 6 & 8 & 7 & α \end{matrix}]$ is of rank $3$ Then $α =$