Matrix Multiplication

How to multiply a 1x3 row by a 3x1 obelisk with the heat onthe left.

You are watching: How to multiply matrices 3x3 and 3x1

����Similarly� we have the right to multiply a 1xnrow through a nx1 column.



We can multiply any mx3 procession by a 3x1 shaft bymultiplying each row of the� mx3 through the3x1 column. Heat 1 the the mx3 multiply by the column gives Row 1 of theproduct. Heat 2 of the mx3 multiply by the column offers Row 2 that the produc t.



Notice the an outcome of multiplying the 2x3 by the 3x1 is a 2x1matrix.

We deserve to multiply any kind of mx3 matrix, A, by any 3xn matrix, B, ifA is on the left side of B.

You will see that ab need not equal BA, even if both have the right to bedone. The product of one mx3 and also a 3xn is one mxnmatrix. Row ns of the product is the result ofmultiplying each row ns of A by each pillar of B.

In short, If AB=C then




�Since A is 2x3 and B is 3x4, abdominal can it is in doneand is 2x4.

If we simply want the entrance in heat 2, obelisk 3 of ab we multiply row 2 that A by column 3 ofB to get

0(-2)+2(-5)+4(3)=0-10+12 = 2

The entirety product is


We can find this in the calculator as follows:� get in matrix A and enter procession B.

MATRIX choose A, enter, MATRIX choose B, enter, enter.

Meanings that MatrixProducts


An upholsterer has actually an order come cover 4 chairs and also 3 sofas.Each chair requires 5 yards of fabric and also 10 hrs of labor. Each sofa requires16 yards of fabric and also 24 hours of laboratory or. Fabric costs $18 per yard, laborcosts $20 per hour. Create a matrix product that offers the complete cost of theorder.

I. Placed the information around fabric and labor requirementsfor chairs and also sofas right into a 2x2 matrix.

Label the rows and also columns so you recognize what the entriesmean. This is additionally important due to the fact that we have actually two selections for setting up thematrix.

Choice 1���� ��������Choice2���


The 2nd matrix is the transpose that the first. The problemcan be operated with one of two people one therefore I will use selection 1 an initial and an option 2 2nd.Where you placed the complying with matrices and how the product looks depends on whichchoice� girlfriend use.

II. Since we have actually chosen choice 1, the information around fabriccost per yard and labor price per hour need to go ~ above the left together a 1x2 row.

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Notice how the labels enhance up.

III. Placed the information�about the number of chairs and sofas bespeak in a 2x1 shaft on theright.