Matrix-Vector Product - Linear Algebra
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Multiply 
Multiply
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To multiply, add:


To multiply, add:
Multiply: 
Multiply:
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To multiply, add:


To multiply, add:
Compute AB.


Compute AB.
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Because the number of columns in matrix A and the number of rows in matrix B are equal, we know that product AB does in fact exist. Matrix AB should have the same number of rows as A and the same number of columns as B. In this case, AB is a 2x3 matrix:

Because the number of columns in matrix A and the number of rows in matrix B are equal, we know that product AB does in fact exist. Matrix AB should have the same number of rows as A and the same number of columns as B. In this case, AB is a 2x3 matrix:
Compute AB


Compute AB
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Because the number of columns in matrix A and the number of rows in matrix B are equal, we know that product AB does in fact exist. Matrix AB should have the same number of rows as A and the same number of columns as B. In this case, AB is a 1x4 matrix:

Because the number of columns in matrix A and the number of rows in matrix B are equal, we know that product AB does in fact exist. Matrix AB should have the same number of rows as A and the same number of columns as B. In this case, AB is a 1x4 matrix:
Calculate
, given
,
Calculate , given
,
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By definition,
.
By definition,
.
Calculate
, given


Calculate , given
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By definition,
. A matrix with only one entry is simply a scalar.
By definition,
. A matrix with only one entry is simply a scalar.
Calculate
, given

.
Calculate , given
.
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By definition,
.
By definition,
.
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Let
be a matrix and
be a vector defined by:


Find the product
.
Let be a matrix and
be a vector defined by:
Find the product .
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First we check the dimensions. The matrix
has 3 columns and the vector
has three rows. The dimensions match and the product exists.

Now we take the dot product of rows in the matrix and the vector
.

First we check the dimensions. The matrix has 3 columns and the vector
has three rows. The dimensions match and the product exists.
Now we take the dot product of rows in the matrix and the vector .