In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form, using different sequences of row operations. is this statement true or false?

This is False.

Step-by-step explanation:

To solve matrices, operations such as the Gaussian elimination can be used. After this operation, a matrix with a row echelon form is obtained. The reduced echelon form is particular case of this, in which the matrix:

1. Is in row echelon form.

2. The first number in each non-zero row is 1 (which is called a leading 1).

3. Each column that has a leading 1 has zeros everywhere else

A matrix in a reduced row echelon form is unique and independent on the algorithm used to calculate it.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

15% chance.

step-by-step explanation:

3/10 times, the 5 year old will get a tablet. 5/10 times, the 13 yer old will get a tablet. multiply both fractions to get 15/100 times, both would have a tablet.