The given matrix equation is false in general. Explain why the equation is false. Assume that all matrices are n ✕ n. (A + B)2 = A2 + 2AB + B2 (A + B)2 = A2 + AB + BA + B2. This is only equal to A2 + 2AB + B2 when AB = −BA, which in general is not true. (A + B)2 = A2 + AB − AB + B2 = A2 + B2. This is only equal to A2 + 2AB + B2 when A = 0nn or B = 0nn, which in general is not true. (A + B)2 = A2 − BA + BA + B2 = A2 + B2. This is only equal to A2 + 2AB + B2 when A = 0nn or B = 0nn, which in general is not true. (A + B)2 = A2 + AB + BA + B2. This is only equal to A2 + 2AB + B2 when AB = BA, which in general is not true. Give a 2 ✕ 2 example showing the equation is false. A = 1 2 3 4

Fourth option is the correct one.

Step-by-step explanation:

Given:

Lets Assume

Now,

if we multiply both in sequence AB, we get

Now if we multiply both in sequence BA, we get

      =  

Hence AB ≠ BA

Now according to equation,

(A+B)² = A² + B² + AB + BA = A² + B² + 2AB only when AB = BA which is not the case as seen in example above

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180