What principle states that if AB 0 then either a 0 or B 0 or both A and B are 0?

What principle states that if AB 0 then either a 0 or B 0 or both A and B are 0?

zero product property
The zero product property states that if a⋅b=0 then either a or b equal zero. This basic property helps us solve equations like (x+2)(x-5)=0.

What is the name of this property if A and B are real numbers and a * b 0 then either a 0 or B 0?

The zero product property, also called zero-product principle, states that for any real numbers a and b, if ab = 0, then either a equals zero, b equals zero, or both a and b equal zero. Since in many cases, there can be more than 2 factors, we can generalize the zero product property as shown below.

Is it possible that if AB 0 then either one of them is non zero matrix?

Thanks for A2A. For two numbers a and b, we know that if ab = 0, then either a = 0 or b = 0. ( i.e. Product of two non-zero numbers is always non-zero). But product of two non-zero matrices can be zero matrix.

Under which conditions can the zero product property be used to solve a polynomial equation choose all that apply?

The zero product property states if ab=0, then a and/or b must be 0. This property lets us solve factored quadratics set equal to 0.

What property is a/b is a real number?

The commutative properties tell you that two numbers can be added or multiplied in any order without affecting the result. Let a and b represent real numbers.

Is matrix AB 0 then?

A must be equal to zero matrix or B must be equal to zero matrix. A must be equal to zero matrix and B must be equal to zero matrix. If matrix AB = 0 then it is not necessary that either A is zero matrix of B is zero matrix.

How do you find the value of AB if a=0?

If a = 0 or b = 0 then ab = 0, which isn’t > 0. Then show if a > 0 and b < 0, that ab < 0, etc. Or you could show if a > 0 then 1/a > 0, and if a < 0 then 1/a < 0, and apply that. For example if a > 0 and ab > 0, then b = (ab) (1/a) > 0.

Is it possible to prove that a <>0 and b <> 0?

In other words, at least one of the numbers a and b must be 0. This means that it impossible to prove that a <> 0 AND b <> 0 as a consequence of the assumption a.b = 0. If the algebraic structure is NOT a field, then a.b = 0 can happen. For instance in the ring Z/ (2. n. Z), n >= 1, the ring with 2. n elements (0, . . . 2.

What is the proof that ab = 0?

We have to show that if ab = 0, then either a = 0 or b = 0, and we have to show that if a = 0 or b = 0, then ab = 0. Let’s do the second one first because it’s easier. Proof: Given a = 0 or b = 0, to show that ab = 0. If we know that 0 times anything is 0, then we can conclude that.

What happens if ab = 0?

If ab = 0 then a = 0 or b = 0. My proof is fairly straightforward. Assume for the sake of contradiction that a is not equal to 0 and b is not equal to 0, when you multiply a and b you get zero, but that is a contradiction because when you multiply two non zero numbe