1:Find the determinant of the following mattrix [2−1−6−305430] 2: If told that matrix A is singular Matrix find the possible value(s) for x A={16x4xx9

Given: A=[2−1−6−305430] As discussed above determinant of A=2(0−3⋅5)−(−1)[−3⋅0−4⋅5]+(−6)[−3⋅3−4⋅0] =2(−15)+1(0−20)−6(−9−0) =−30−20+54=4 Hence, he determinant of the given matrix=4 c.A=[16x4xx9] We know when the matrix is single determinant is zero Calculating the determinant of A |A|=16⋅9−x⋅4x =144−4x2 Now, put |A|=0 i.e, 144−4x2=0 4x2=144 x2=1444=36 x2=36⇒x=(36) x=6 Hence, x=−6 or x=6 (−6,=6)

Resolved: "1:Find the determinant of the following mattrix [2−1−6−305430]..."

College
Algebra
Linear algebra
Matrix transformations

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Answered question

2021-02-06

1:Find the determinant of the following mattrix $[\begin{matrix} \begin{matrix} 2 & - 1 & - 6 \end{matrix} \\ \begin{matrix} - 3 & 0 & 5 \end{matrix} \\ \begin{matrix} 4 & 3 & 0 \end{matrix} \end{matrix}]$

2: If told that matrix A is singular Matrix find the possible value(s) for x $A = {\begin{matrix} 16 x & 4 x \\ x & 9 \end{matrix}$

Answer & Explanation

Anonym

Skilled2021-02-07Added 108 answers

Given:
$A = [\begin{matrix} 2 & - 1 & - 6 \\ - 3 & 0 & 5 \\ 4 & 3 & 0 \end{matrix}]$
As discussed above determinant of $A = 2 (0 - 3 \cdot 5) - (- 1) [- 3 \cdot 0 - 4 \cdot 5] + (- 6) [- 3 \cdot 3 - 4 \cdot 0]$
$= 2 (- 15) + 1 (0 - 20) - 6 (- 9 - 0)$
$= - 30 - 20 + 54 = 4$
Hence, he determinant of the given matrix=4
$c . A = [\begin{matrix} 16 x & 4 x \\ x & 9 \end{matrix}]$
We know when the matrix is single determinant is zero
Calculating the determinant of A
$| A | = 16 \cdot 9 - x \cdot 4 x$
$= 144 - 4 x^{2}$
Now, put $| A | = 0$
i.e,
$144 - 4 x^{2} = 0$
$4 x^{2} = 144$
$x^{2} = \frac{144}{4} = 36$
$x^{2} = 36 \Rightarrow x = \sqrt{(} 36)$
$x = 6$
Hence, $x = - 6$ or $x = 6$
$(- 6, = 6)$

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