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3 years ago

Is parallelogram a rectangle

2 answers:

8 0

A parallelogram is usually defined as a quadrilateral with 2 pairs of equal, opposite and parallel sides. It can also form right angles between adjacent sides. Therefore, not all rectangles are squares, not all parallelograms are rectangles.

Hope I could help! :)

denis-greek [22]3 years ago

4 0

Answer:

Sometimes, but not always.

Step-by-step explanation:

A parallelogram is a quadrilateral with two pairs of parallel sides, but there are no requirements for its interior angles. A rectangle, on the other hand, <em>must</em> have four interior 90 degree angles. So a rectangle is always a parallelogram, but a parallelogram is not always a rectangle.

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2 years ago

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2 years ago

An n × n matrix B has characteristic polynomial p(λ) = −λ(λ − 3) 3 (λ − 2) 2 (λ + 1). Which of the following statements is false

asambeis [7]

Answer:

Only d) is false.

Step-by-step explanation:

Let $p=p(\lambda)=\lambda(\lambda-3)^3 (\lambda-2)^2 (\lambda+1)$ be the characteristic polynomial of B.

a) We use the rank-nullity theorem. First, note that 0 is an eigenvalue of algebraic multiplicity 1. The null space of B is equal to the eigenspace generated by 0. The dimension of this space is the geometric multiplicity of 0, which can't exceed the algebraic multiplicity. Then Nul(B)≤1. It can't happen that Nul(B)=0, because eigenspaces have positive dimension, therfore Nul(B)=1 and by the rank-nullity theorem, rank(B)=7-nul(B)=6 (B has size 7, see part e)

b) Remember that $p(\lambda)=\det(B-\lambda I)$ . 0 is a root of p, so we have that $p(0)=\det(B-0 I)=\det B=0$ .

c) The matrix T must be a nxn matrix so that the product BTB is well defined. Therefore det(T) is defined and by part c) we have that det(BTB)=det(B)det(T)det(B)=0.

d) det(B)=0 by part c) so B is not invertible.

e) The degree of the characteristic polynomial p is equal to the size of the matrix B. Summing the multiplicities of each root, p has degree 7, therefore the size of B is n=7.

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3 years ago

Multiply 3/7 by the reciprocal of -3/14

Alexandra [31]

Multiplying 3/7 by the reciprocal of -3/14,

$\frac{3}{7} \times \frac{14}{ - 3} \\ = \frac{1}{1} \times \frac{2}{ - 1} \\ = \frac{2}{ - 1} \\ = - 2$

Hope it helps!!

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3 years ago