Understanding Matrix Multiplication

Why does the order of multiplication matter in matrix multiplication?

• Because it affects the dimensions of the resulting matrix

• Because it has no effect on the outcome

• Because it changes the numerical values within the matrices

• Because it alters the original matrices

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CCSS.HSN.VM.C.9

What is the result of multiplying a 1x3 matrix by a 3x1 matrix?

• A 2x2 matrix

• A 1x1 matrix

• A 3x3 matrix

• A 3x1 matrix

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CCSS.HSN.VM.C.8

CCSS.HSN.VM.C.9

What condition must be met to multiply two matrices?

• The matrices must have the same dimensions

• The number of rows in the first matrix must equal the number of columns in the second

• The number of columns in the first matrix must equal the number of rows in the second

• The matrices must be square

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CCSS.HSN.VM.C.8

What does a 1x1 matrix result from?

• Multiplying two matrices of the same order

• Adding two matrices of any order

• Multiplying a 1x3 matrix by a 3x1 matrix

• Multiplying two square matrices

What is the significance of the order of matrices in multiplication?

• It changes the shape of the original matrices

• It affects the color of the matrices

• It determines the numerical values in the resulting matrix

• It has no significance

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CCSS.HSN.VM.C.9

What is the order of the matrix resulting from multiplying a 3x1 matrix by a 1x3 matrix?

• 1x1

• 1x3

• 3x3

• 2x2

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CCSS.HSN.VM.C.8

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In matrix multiplication, if the product AB is defined, is BA always defined?

• No, not necessarily

• Yes, but only for square matrices

• Yes, always

• No, BA is never defined

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CCSS.HSN.VM.C.9

Can a 3x4 matrix be multiplied by a 2x3 matrix?

• Yes, without any conditions

• No, because their orders are incompatible

• Yes, but only if the 3x4 matrix is transposed first

• No, because matrix multiplication is not defined for these dimensions

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CCSS.HSN.VM.C.8

What happens if you try to multiply matrices with incompatible orders?

• The matrices automatically adjust their orders

• The multiplication is undefined

• The product is a matrix of zeros

• The multiplication proceeds with a warning

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CCSS.HSN.VM.C.8

CCSS.HSN.VM.C.9

What is the order of the product when a 2x3 matrix is multiplied by a 3x4 matrix?

• 3x4

• 4x2

• 3x3

• 2x4

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CCSS.HSN.VM.C.8

CCSS.HSN.VM.C.9