Question

Suppose that the three numbers $r_1$, $r_2$, and $r_3$ are distinct. Show that the three functions exp ($r_1$x), exp ($r_2$x), and exp ($r_3$x) are linearly independent by showing that their Wronskian given below is nonzero for all x. $W = \exp[ (r_1 + r_2 + r_3)x] \cdot \begin{vmatrix} 1 & 1 & 1 \ r_1 & r_2 & r_3 \ r_1^2 & r_2^2 & r_3^2 \end{vmatrix}$ Yes No The other factor involves the numbers $r_1$, $r_2$, and $r_3$. This can be further factored as a product of binomials. $W = \exp[ (r_1 + r_2 + r_3)x] \cdot \boxed{\text{(Factor completely.)}}$

          Suppose that the three numbers $r_1$, $r_2$, and $r_3$ are distinct. Show that the three functions exp ($r_1$x), exp ($r_2$x), and exp ($r_3$x) are linearly independent by showing that their Wronskian given below is nonzero for all x.

$W = \exp[ (r_1 + r_2 + r_3)x] \cdot \begin{vmatrix} 1 & 1 & 1 \ r_1 & r_2 & r_3 \ r_1^2 & r_2^2 & r_3^2 \end{vmatrix}$

Yes
No

The other factor involves the numbers $r_1$, $r_2$, and $r_3$. This can be further factored as a product of binomials.

$W = \exp[ (r_1 + r_2 + r_3)x] \cdot \boxed{\text{(Factor completely.)}}$

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Suppose that the three numbers r1, r2, and r3 are distinct. Show that the three functions exp (r1x), exp (r2x), and exp (r3x) are linearly independent by showing that their Wronskian given below is nonzero for all x.

W = [ (r1 + r2 + r3)x] · 1 1 1 r1 r2 r3 r1^2 r2^2 r3^2

Yes
No

The other factor involves the numbers r1, r2, and r3. This can be further factored as a product of binomials.

W = [ (r1 + r2 + r3)x] ·(Factor completely.)

Added by Sonia R.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Raj Bala

01/24/2022

Step 1

Step 1: The Wronskian of the functions exp(r1), exp(r2), and exp(r3) is given by: W = det | exp(r1x) exp(r2x) exp(r3x) | | r1exp(r1x) r2exp(r2x) r3exp(r3x) | | r1^2exp(r1x) r2^2exp(r2x) r3^2exp(r3x) | Show more…

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The other factor involves the numbers r1, r2, and r3. This can be further factored as a product of binomials. Suppose that the three numbers r1, r2, and r3 are distinct. Show that the three functions exp (r1), exp (r2), and exp (r3) are linearly independent by showing that their Wronskian given below is nonzero for all x. W=exp[(r1+r2+r3)x] r1r2 Yes or No The other factor involves the numbers r1, r2, and r3. This can be further factored as a product of binomials. ((eodwo Ipoey)[x(++i)] dx=

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