Verify that the vector X is a solution of the given homogeneous system. X' = (−1 1 1/25 -1)X; X = (−1 5)e−6t/5
For X = (−1 5)e−6t/5, one has
Since the above expressions, X = (−1 5)e−6t/5 is a solution of the given system.
The given vectors are solutions of a system X' = AX. Determine whether the vectors form a fundamental set on the interval (-co, o).
X1 = (1 -2 4) + t(1 2 2), X2 = (1 -2 4), X3 = (2 -4 8) + t(4 4 8)
A. Yes, since the set X,, X,, X3 is linearly independent for -o B. Yes, since the set X,, X2, X3 is linearly dependent for -t C. No, since the set X,, X2, X3 is linearly independent for -co t<.
D. No, since the set X, X2, X, is linearly dependent for -oo

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

If i think this is what your asking, he should look at the grams or pounds/ounces and compare the to their cost then max can identify which one is proportional and which is not ( i think xd)