Matrix Operations Quiz for Grade 10

Subtract

• 3    -8
  0   -1

• 3   -4
  8  -13

• -3   8
  0    1

• 3   -8
  -8    1

Answer explanation

To subtract, calculate 3 - 4 = -1 and 8 - 13 = -5. The correct choice is 3 - 4 and 8 - 13, which gives the results -1 and -5 respectively.

The matrix N - N is

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• 
• 
• 

Tags

CCSS.HSN.VM.C.8

Add the matrices: \[ A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} \]

Answer explanation

To add matrices A and B, sum corresponding elements: \[ A + B = \begin{bmatrix} 1+5 & 2+6 \ 3+7 & 4+8 \end{bmatrix} = \begin{bmatrix} 6 & 8 \ 10 & 12 \end{bmatrix} \]. Thus, the correct answer is \( \begin{bmatrix} 6 & 8 \ 10 & 12 \end{bmatrix} \).

Tags

CCSS.HSN.VM.C.6

CCSS.HSN.VM.C.8

Subtract the matrices: \[ A = \begin{bmatrix} 9 & 8 \\ 7 & 6 \end{bmatrix}, \quad B = \begin{bmatrix} 5 & 4 \\ 3 & 2 \end{bmatrix} \]

Answer explanation

To subtract matrices A and B, subtract corresponding elements: \[ A - B = \begin{bmatrix} 9-5 & 8-4 \ 7-3 & 6-2 \end{bmatrix} = \begin{bmatrix} 4 & 4 \ 4 & 4 \end{bmatrix} \]. Thus, the correct answer is \( \begin{bmatrix} 4 & 4 \ 4 & 4 \end{bmatrix} \).

Tags

CCSS.HSN.VM.C.6

CCSS.HSN.VM.C.8

Multiply the matrix by a scalar: \[ 3 \times \begin{bmatrix} 2 & 0 \\ 1 & -1 \end{bmatrix} \]

Answer explanation

To multiply the matrix by the scalar 3, multiply each element: \[ 3 \times 2 = 6, \ 3 \times 0 = 0, \ 3 \times 1 = 3, \ 3 \times -1 = -3 \]. Thus, the result is \[ \begin{bmatrix} 6 & 0 \ 3 & -3 \end{bmatrix} \].

Tags

CCSS.HSN.VM.C.7

CCSS.HSN.VM.C.8

Identify the dimensions of the matrix: \[ A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \]

Answer explanation

The matrix A has 2 rows and 3 columns, which gives it dimensions of 2 x 3. Therefore, the correct choice is 2 \times 3.

Multiply the matrices: \[ A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 2 & 0 \\ 1 & 2 \end{bmatrix} \]

Answer explanation

To multiply matrices A and B, calculate each element: \(C_{11} = 1*2 + 2*1 = 4\), \(C_{12} = 1*0 + 2*2 = 4\), \(C_{21} = 3*2 + 4*1 = 10\), \(C_{22} = 3*0 + 4*2 = 8\). Thus, \(C = \begin{bmatrix} 4 & 4 \ 10 & 8 \end{bmatrix}\).

Tags

CCSS.HSN.VM.C.8

CCSS.HSN.VM.C.9

Determine if the following matrix is a square matrix: \[ A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \]

• Yes

• No

Answer explanation

A square matrix has the same number of rows and columns. The matrix A has 2 rows and 2 columns, making it a square matrix. Therefore, the correct answer is Yes.

Add the matrices: \[ A = \begin{bmatrix} 0 & 1 \\ 2 & 3 \end{bmatrix}, \quad B = \begin{bmatrix} 4 & 5 \\ 6 & 7 \end{bmatrix} \]

Answer explanation

To add matrices A and B, sum corresponding elements: \[ A + B = \begin{bmatrix} 0+4 & 1+5 \ 2+6 & 3+7 \end{bmatrix} = \begin{bmatrix} 4 & 6 \ 8 & 10 \end{bmatrix} \]. Thus, the correct answer is \( \begin{bmatrix} 4 & 6 \ 8 & 10 \end{bmatrix} \).

Tags

CCSS.HSN.VM.C.8

Subtract the matrices: \[ A = \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \]

Answer explanation

To subtract matrices A and B, subtract corresponding elements: \[ A - B = \begin{bmatrix} 5-1 & 6-2 \ 7-3 & 8-4 \end{bmatrix} = \begin{bmatrix} 4 & 4 \ 4 & 4 \end{bmatrix} \]. Thus, the correct answer is \( \begin{bmatrix} 4 & 4 \ 4 & 4 \end{bmatrix} \).

Tags

CCSS.HSN.VM.C.8