[$._("Yes"), $._("No")] DEFINED ? YES : NO makeMatrix(randRange(-2, 4, DIM_1, DIM_2)) makeMatrix(randRange(-2, 4, DIM_3, DIM_4)) "\\textbf " + randFromArray("ABCDEF") "\\textbf " + randFromArray("ABCDEF") printSimpleMatrix(MAT_1) printSimpleMatrix(MAT_2)

`PRETTY_MAT_1_ID = PRETTY_MAT_1`

`PRETTY_MAT_2_ID = PRETTY_MAT_2`

Is `PRETTY_MAT_1_ID + OPERATION + PRETTY_MAT_2_ID` defined?

ANSWER

- YES
- NO

randRange(0, 1) randRange(1, 3) randRange(1, 3) DIM_1 DEFINED ? DIM_2 : randRangeExclude(1, 3, [DIM_2]) randFromArray("+-")

In order for addition of two matrices to be defined, the matrices must have the same dimensions.

If `PRETTY_MAT_1_ID` is of dimension `(\blue m \times \red n)` and `PRETTY_MAT_2_ID` is of dimension `(\blue p \times \red q)`, then for their sum to be defined:

In order for subtraction of two matrices to be defined, the matrices must have the same dimensions.

If `PRETTY_MAT_1_ID` is of dimension `(\blue m \times \red n)` and `PRETTY_MAT_2_ID` is of dimension `(\blue p \times \red q)`, then for their difference to be defined:

1. `\blue m` (number of rows in `PRETTY_MAT_1_ID`) must equal `\blue p` (number of rows in `PRETTY_MAT_2_ID`) and

2. `\red n` (number of columns in `PRETTY_MAT_1_ID`) must equal `\red q` (number of columns in `PRETTY_MAT_2_ID`)

Do `PRETTY_MAT_1_ID` and `PRETTY_MAT_2_ID` have the same number of rows?

DIM_1 === DIM_3 ? YES : NO

YES NO

Do `PRETTY_MAT_1_ID` and `PRETTY_MAT_2_ID` have the same number of columns?

DIM_2 === DIM_4 ? YES : NO

YES NO

Since `PRETTY_MAT_1_ID` has the same dimensions `(DIM_1 + "\\times" + DIM_2)` as `PRETTY_MAT_2_ID` `(DIM_3 + "\\times" + DIM_4)`, `PRETTY_MAT_1_ID + OPERATION + PRETTY_MAT_2_ID` is defined.

Since `PRETTY_MAT_1_ID` has different dimensions `(DIM_1 + "\\times" + DIM_2)` from `PRETTY_MAT_2_ID` `(DIM_3 + "\\times" + DIM_4)`, `PRETTY_MAT_1_ID + OPERATION + PRETTY_MAT_2_ID` is not defined.

randRange(0, 1) randRange(1, 3) randRange(1, 3) DEFINED ? DIM_2 : randRangeExclude(1, 3, [DIM_2]) randRange(1, 3) ""

In order for multiplication of two matrices to be defined, the two inner dimensions must be equal.

If the two matrices have dimensions `(\blue m \times \red n)` and `(\red p \times \green q)`, then `\red n` (number of columns in the first matrix) must equal `\red p` (number of rows in the second matrix) for their product to be defined.

How many columns does the first matrix, `PRETTY_MAT_1_ID`, have?

DIM_2

How many rows does the second matrix, `PRETTY_MAT_2_ID`, have?

DIM_3

Since `PRETTY_MAT_1_ID` has the same number of columns (DIM_2) as `PRETTY_MAT_2_ID` has rows (DIM_3), `PRETTY_MAT_1_ID + PRETTY_MAT_2_ID` is defined.
Since `PRETTY_MAT_1_ID` has a different number of columns (DIM_2) than `PRETTY_MAT_2_ID` has rows (DIM_3), `PRETTY_MAT_1_ID + PRETTY_MAT_2_ID` is not defined.