How To Multiply Matrices Of Different Sizes

Matrix multiplication falls into ii general categories:

1. Scalar: in which a single number is multiplied with every entry of a matrix.
2. Multiplication of ane matrix past 2nd matrix.

   For the rest of the page, matrix multiplication will refer to this second category.

Part I. Scalar Matrix Multiplication

In the scalar variety, every entry is multiplied by a number, called a scalar. In the post-obit example, the scalar value is $$ \blue 3 $$.

$ \blue 3 \brainstorm{bmatrix} 5 & 2 & 11 \\ 9 & 4 & 14 \\ \end{bmatrix} = \begin{bmatrix} \blue three \cdot five & \blue three \cdot 2 & \blue three \cdot 11 \\ \bluish 3 \cdot 9 & \blue three \cdot 4 & \blue 3 \cdot 14 \\ \stop{bmatrix} \\ = \begin{bmatrix} 15 & half dozen & 33 \\ 27 & 12 & 42 \\ \end{bmatrix} $

Multiply the matrix below by $$2$$

Tin you figure out the reply to the scalar multiplication problem beneath? (hint: just multiply every entry past $$two$$)

When can yous multiply one matrix by another matrix?

You can multiply two matrices if, and simply if, the number of columns in the showtime matrix equals the number of rows in the 2d matrix. (Link on columns vs rows )

In the flick above , the matrices can be multiplied since the number of columns in the 1st one, matrix A, equals the number of rows in the ii^nd, matrix B.

Two Matrices that can non exist multiplied

Matrix A and B below cannot be multiplied together considering the number of columns in A $$ \ne $$ the number of rows in B. In this case, the multiplication of these two matrices is not defined.

Another example of 2 matrices you can not multiply

Matrix C and D below cannot be multiplied.

Can the two matrices below be multiplied?

No

Since the number of columns in Matrix A does non equal the number of rows in Matrix B.

The multiplication of A and B is undefined.

So, what are the dimensions of the production matrix?

The production matrix'southward dimensions are (rows of start matrix) × (columns of the second matrix).

OK, so how practice nosotros multiply two matrices?

In order to multiply matrices,

• Step one: Make sure that the the number of columns in the ane^st ane equals the number of rows in the 2^nd one. (The pre-requisite to be able to multiply)
• Stride 2: Multiply the elements of each row of the showtime matrix by the elements of each column in the 2nd matrix.
• Pace 3: Add together the products.

It's easier to empathize these steps, if you go through interactive demonstrations beneath.

Step Past Stride Demonstrations

Practice Problems

Problem 1

Problem 2

Problem 3

How To Multiply Matrices Of Different Sizes,

Source: https://www.mathwarehouse.com/algebra/matrix/multiply-matrix.php

Posted by: bryantwarajected.blogspot.com

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