Show that there are infinitely many vectors in R with Euclidean norm 1 whose Euclidean inner product with (1, –2,4) is zero.
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
Solve number 18 please
 alt="Problem related to Euclidean Space and Linear Transformation:
Show that there are infinitely many vectors in R’with Euclidean norm 1 whose Euclidean inner
product with (1, –2,4) is zero.
18.
Find two vectors of norm 1 that are orthogonal to the vectors u =
w = (3,2,5,4).
(2,1, –4,0), v = (-1,-1,2,2), and
19.
Find the standard matrix for the linear operator T:R³ → R³ that first rotate a vector counterclockwise
about the y-axis through an angle 0 = 60, then reflect the resulting vector about the xz -plane, and
then transform the resulting vector by the formula T(x,y,z) = (2x – 3y + 4z, –3x + y – 2z,x +
3y). Hence compute T(1, –2,1).
20.
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