Matrix Addition - Revision history

Thakshashila: /* ✅ Final Answer */

2025-05-23T08:09:59Z

✅ Final Answer

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 \end{bmatrix}
 </math>
 == Important Properties of Matrix Addition ==

Thakshashila: /* ✅ Final Answer */

2025-05-23T08:09:26Z

✅ Final Answer

← Older revision		Revision as of 08:09, 23 May 2025
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	<math>		<math>
	\boxed{		\boxed{
	\begin{~~bmatrix~~}		\left[
			\begin{array}{ccc}
	9 & 5 & 9 \\		9 & 5 & 9 \\
	5 & 3 & 7		5 & 3 & 7
	\end{~~bmatrix~~}		\end{array}
			\right]
	}		}
	</math>		</math>

	Meaning		Meaning

Thakshashila: /* ✅ Final Answer */

2025-05-23T08:08:46Z

✅ Final Answer

← Older revision		Revision as of 08:08, 23 May 2025
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	== ✅ Final Answer ==		== ✅ Final Answer ==
			<math>
	\boxed{		\boxed{
	\begin{bmatrix}		\begin{bmatrix}
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	\end{bmatrix}		\end{bmatrix}
	}		}
	~~Meanin~~		</math>
			Meaning

	== Important Properties of Matrix Addition ==		== Important Properties of Matrix Addition ==

Thakshashila: /* ✅ Final Answer */

2025-05-23T08:08:09Z

✅ Final Answer

← Older revision		Revision as of 08:08, 23 May 2025
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	== ✅ Final Answer ==		== ✅ Final Answer ==

	~~<math>~~
	\boxed{		\boxed{
	\begin{bmatrix}		\begin{bmatrix}
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	\end{bmatrix}		\end{bmatrix}
	}		}
	~~</math>~~		Meanin

	== Important Properties of Matrix Addition ==		== Important Properties of Matrix Addition ==

Thakshashila at 08:07, 23 May 2025

2025-05-23T08:07:23Z

← Older revision		Revision as of 08:07, 23 May 2025
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	= Matrix Addition =		= Matrix Addition – Step-by-Step Explanation =

	Matrix addition is ~~the process~~ of adding ~~two~~ matrices of the ~~'''~~same dimensions~~''' by adding their corresponding elements~~.		Matrix addition is a method of combining two matrices by adding the elements that are in the same position. This operation is only defined when both matrices have the same dimensions (same number of rows and columns).

	== ~~Conditions for~~ Matrix ~~Addition~~ ==		== Step 1: Understand Matrix Dimensions ==

	~~Two matrices can be added only if they have~~ the ~~same~~ number of rows and ~~the same number of~~ columns.		Each matrix has an "order" or "size" defined by the number of rows and columns it has.
			A matrix with 2 rows and 3 columns is a 2×3 matrix.

	~~For example, if~~:		'''Example:'''
	* Matrix A is of order 2×3
	* Matrix B must also be of order 2×3 to be added to A

	~~== Rule for Addition ==~~		Let’s take two matrices A and B:

	~~If:~~
	~~<math>~~
	A ~~= [a_{ij}], \quad~~ B ~~= [b_{ij}]~~
	~~</math>~~

	~~Then:~~
	~~<math>~~
	~~A + B = [a_{ij} + b_{ij}]~~
	~~</math>~~

	~~This means we add each element of matrix A with the corresponding element in matrix B.~~

	~~== Step-by-Step Example ==~~

	~~Let~~:

	<math>		<math>
Line 40:		Line 23:
	</math>		</math>

	~~'''~~Step 1:~~''' Check that both matrices have~~ the same ~~order.~~		Matrix A is a 2×3 matrix (2 rows, 3 columns)
	~~Both A and B are 2×3 matrices~~ → ~~✅ OK~~		Matrix B is also a 2×3 matrix
			→ ✅ Same size ⇒ Matrix addition is possible

			== Step 2: Identify Corresponding Elements ==

			Matrix addition is performed by adding corresponding elements in each position.

			So we pair each element in matrix A with the one in matrix B at the same location:

			* (1,1) → <math>2 + 7</math>
			* (1,2) → <math>4 + 1</math>
			* (1,3) → <math>6 + 3</math>
			* (2,1) → <math>1 + 4</math>
			* (2,2) → <math>3 + 0</math>
			* (2,3) → <math>5 + 2</math>

	~~'''~~Step 2:~~''' Add corresponding elements~~:		== Step 3: Perform the Addition ==

			Now add each pair:

	<math>		<math>
	~~A + B =~~ \begin{~~bmatrix~~}		\begin{aligned}
	2+7 & 4+1 & 6+3 \\		2 + 7 &= 9 \\
	1+4 & 3+0 & 5+2		4 + 1 &= 5 \\
	\end{~~bmatrix~~}		6 + 3 &= 9 \\
			1 + 4 &= 5 \\
			3 + 0 &= 3 \\
			5 + 2 &= 7
			\end{aligned}
	</math>		</math>

	~~'''~~Step 3:~~''' Perform~~ the ~~additions~~:		== Step 4: Write the Resulting Matrix ==

			Now place the results in their original positions to form the new matrix:

	<math>		<math>
Line 61:		Line 66:
	</math>		</math>

	== Final Answer ==		== ✅ Final Answer ==

	<math>		<math>
			\boxed{
	\begin{bmatrix}		\begin{bmatrix}
	9 & 5 & 9 \\		9 & 5 & 9 \\
	5 & 3 & 7		5 & 3 & 7
	\end{bmatrix}		\end{bmatrix}
			}
	</math>		</math>

	~~---~~		== Important Properties of Matrix Addition ==

			* '''Commutative Law''': <math>A + B = B + A</math>
			* '''Associative Law''': <math>(A + B) + C = A + (B + C)</math>
			* The '''zero matrix''' <math>O</math> acts like 0:
			<math>A + O = A</math>

			== Summary ==

	~~== Important Notes ==~~		To add matrices:
	* You cannot add matrices ~~of different dimensions.~~		1. Confirm that both matrices are the same size.
	* Matrix addition is commutative:		2. Add elements in corresponding positions.
	~~<math>~~		3. Write the results in a new matrix of the same size.
	~~A + B = B + A~~
	~~</math>~~
	* It is also associative:
	~~<math>~~
	~~(A + B) + C = A + (B + C)~~
	~~</math>~~

	---		---

	''Matrix addition is a ~~simple but essential operation~~ in ~~linear~~ algebra ~~and is widely used in computer~~ science~~, engineering~~, and ~~physics.~~''		''Matrix addition is a basic yet powerful tool used in algebra, data science, and applied mathematics!''

Thakshashila: Created page with "= Matrix Addition = Matrix addition is the process of adding two matrices of the '''same dimensions''' by adding their corresponding elements. == Conditions for Matrix Addition == Two matrices can be added only if they have the same number of rows and the same number of columns. For example, if: * Matrix A is of order 2×3 * Matrix B must also be of order 2×3 to be added to A == Rule for Addition == If: $A = [a_{ij}], \quad B = [b_{ij}]$ Then: $..."$

2025-05-23T08:05:26Z

Created page with "= Matrix Addition = Matrix addition is the process of adding two matrices of the '''same dimensions''' by adding their corresponding elements. == Conditions for Matrix Addition == Two matrices can be added only if they have the same number of rows and the same number of columns. For example, if: * Matrix A is of order 2×3 * Matrix B must also be of order 2×3 to be added to A == Rule for Addition == If: <math> A = [a_{ij}], \quad B = [b_{ij}] </math> Then: <math>..."

New page

= Matrix Addition =

Matrix addition is the process of adding two matrices of the '''same dimensions''' by adding their corresponding elements.

== Conditions for Matrix Addition ==

Two matrices can be added only if they have the same number of rows and the same number of columns.

For example, if:
* Matrix A is of order 2×3
* Matrix B must also be of order 2×3 to be added to A

== Rule for Addition ==

If:
<math>
A = [a_{ij}], \quad B = [b_{ij}]
</math>

Then:
<math>
A + B = [a_{ij} + b_{ij}]
</math>

This means we add each element of matrix A with the corresponding element in matrix B.

== Step-by-Step Example ==

Let:

<math>
A = \begin{bmatrix}
2 & 4 & 6 \\
1 & 3 & 5
\end{bmatrix}, \quad
B = \begin{bmatrix}
7 & 1 & 3 \\
4 & 0 & 2
\end{bmatrix}
</math>

'''Step 1:''' Check that both matrices have the same order.
Both A and B are 2×3 matrices → ✅ OK

'''Step 2:''' Add corresponding elements:

<math>
A + B = \begin{bmatrix}
2+7 & 4+1 & 6+3 \\
1+4 & 3+0 & 5+2
\end{bmatrix}
</math>

'''Step 3:''' Perform the additions:

<math>
A + B = \begin{bmatrix}
9 & 5 & 9 \\
5 & 3 & 7
\end{bmatrix}
</math>

== Final Answer ==

<math>
\begin{bmatrix}
9 & 5 & 9 \\
5 & 3 & 7
\end{bmatrix}
</math>

---

== Important Notes ==
* You cannot add matrices of different dimensions.
* Matrix addition is commutative:
<math>
A + B = B + A
</math>
* It is also associative:
<math>
(A + B) + C = A + (B + C)
</math>

---

''Matrix addition is a simple but essential operation in linear algebra and is widely used in computer science, engineering, and physics.''