A multiple-choice quiz
by Matthew_07.
Estimated time: 5 mins.

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Scroll down to the bottom for the answer key.

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Sep 23 2023 : AdamM7: 7/10

Sep 09 2023 : kaddarsgirl: 4/10

Sep 03 2023 : Guest 122: 2/10

Aug 25 2023 : Guest 94: 2/10

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Quiz Answer Key and Fun Facts

Answer:
**(A+B)^2 = A^2 + 2AB + B^2**

In general, (A+B)^2 is not equal to A^2 + 2AB + B^2, unless AB = BA. Actually, (A+B)^2 = (A+B)(A+B) = A^2 + AB + BA + B^2. The order of arrangement in matrix multiplication operation is very important, unlike the normal real number multiplication operation. We can write 6 = 1 x 6 = 6 x 1, but usually, AB is not equal to BA.

In general, (A+B)^2 is not equal to A^2 + 2AB + B^2, unless AB = BA. Actually, (A+B)^2 = (A+B)(A+B) = A^2 + AB + BA + B^2. The order of arrangement in matrix multiplication operation is very important, unlike the normal real number multiplication operation. We can write 6 = 1 x 6 = 6 x 1, but usually, AB is not equal to BA.

Answer:
**A nonsingular matrix**

All elementary matrices are nonsingular, meaning that they all have their inverse pairs.

All elementary matrices are nonsingular, meaning that they all have their inverse pairs.

Answer:
**Adjoint**

The formula is given by A^-1 = (1/|A|) x Adj (A), where A^-1 is the inverse matrix, |A| is the matrix's determinant, and Adj(A) is the adjoint of the matrix.

The formula is given by A^-1 = (1/|A|) x Adj (A), where A^-1 is the inverse matrix, |A| is the matrix's determinant, and Adj(A) is the adjoint of the matrix.

Answer:
**A = A^-1**

In general, A is not equal to A^-1. Besides, it is interesting to note that (AB)^-1 = (B^-1)(A^-1), and (AB)^T = (B^T)(A^T).

In general, A is not equal to A^-1. Besides, it is interesting to note that (AB)^-1 = (B^-1)(A^-1), and (AB)^T = (B^T)(A^T).

Answer:
**The number of nonzero rows in its row echelon form.**

The rank of a matrix, either in its row echelon form, or its reduced row echelon form, is the same.

The rank of a matrix, either in its row echelon form, or its reduced row echelon form, is the same.

Answer:
**rank (A) < rank (A/B)**

A system that has a unique solution is in the form of rank (A) equals to rank (A|B) equals to n. On the other hand, the one that has infinitely many solutions is in the form of rank (A) equals to rank (A|B) less than n. Notice that rank (A) for an augmented matrix (A|B) is always equals or smaller than rank (A|B). Hence, it is impossible to have the inequality of rank (A) > rank (A|B).

A system that has a unique solution is in the form of rank (A) equals to rank (A|B) equals to n. On the other hand, the one that has infinitely many solutions is in the form of rank (A) equals to rank (A|B) less than n. Notice that rank (A) for an augmented matrix (A|B) is always equals or smaller than rank (A|B). Hence, it is impossible to have the inequality of rank (A) > rank (A|B).

Answer:
**A^T = -A**

For example, A + A^T is a symmetric matrix, because (A + A^T)^T = A^T + (A^T)^T = A^T + A = A + A^T.

For example, A + A^T is a symmetric matrix, because (A + A^T)^T = A^T + (A^T)^T = A^T + A = A + A^T.

Answer:
**Squaring all values in a row**

These 3 operations are called the elementary row operations (ERO).

These 3 operations are called the elementary row operations (ERO).

Answer:
**Not unique; unique**

Some additional steps can be carried on to reduce a row echelon form of a matrix to its reduced row echelon form.

Some additional steps can be carried on to reduce a row echelon form of a matrix to its reduced row echelon form.

Answer:
**Lower-Upper**

It means lower triangular and upper triangular matrices. By writing AX=B in LUX=B, we let Y = UX, we get LY = B. We can then easily find the values of elements in the matrix Y. Next, we solve for all the values in X using the equation Y = UX.

It means lower triangular and upper triangular matrices. By writing AX=B in LUX=B, we let Y = UX, we get LY = B. We can then easily find the values of elements in the matrix Y. Next, we solve for all the values in X using the equation Y = UX.

This quiz was reviewed by FunTrivia editor crisw before going online.

Any errors found in FunTrivia content are routinely corrected through our feedback system.

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