Math Problem Statement
Reshuffle the questions and choice and change some given numbers here is the questions "1.What is the correct term used to describe
each individual number in a matrix?
A. Row B. Column
C. Member D. Dimension
2. If matrix 𝐴 has 3 rows and 4 columns, what is
the dimension of matrix 𝐴?
A. 3 × 3 B. 4 × 3
C. 3 × 4 D. 4 × 4
3.What is the value of 𝑎23 in the matrix
A=
2 0 1
1 3 2
5 7 5
?
A. 2 B. 0
C. 1 D. 5
4.Given the matrices 4 𝑥 𝑦
𝑥 𝑥 𝑧
4 5
2 𝑦 , what
is the value of y?
A. 2 B. 5
C. 3 D. 6
5.Given the matrices 4 𝑥 𝑦
𝑥 𝑥 𝑧
4 5
2 𝑦 , what
is the value of x+y+z?
A. 2 B. 5
C. 3 D. 6
6.Given that
3 3
10
9
4
n
m
n
m
, find the
values of m and n.
A. 4 , 2 n m B. 3 , 2 n m
C. 4 , 2 n m D. 3 , 2 n m
7.Given that matrix
3 5
2 2 3 E ,
4 8
7 6 2 F , find the value of E – F.
A.
1 1
8 18 B.
17 1
20 8
C.
17 1
20 8 D.
1 31
8 18
8. Evaluate
1 5
0 3 3 2 ?
A. 7 3 B.
7
3
C. 3 9 D.
3
9
9.Which of the following is an inverse matrix
[Aij]-1 of A=
5 1
9 2 .
A.
5 9
1 2 B.
19
17
19
1
19
9
19
2
C.
1 0
0 1 D.
2 1
9 5 "
Solution
Here is a reshuffled version of your questions, with some changes to the numbers:
-
If matrix 𝐵 has 4 rows and 2 columns, what is the dimension of matrix 𝐵?
- A. 4 × 4
- B. 2 × 4
- C. 4 × 2
- D. 2 × 2
-
What is the value of 𝑎32 in the matrix
\begin{pmatrix} 3 & 1 & 0 \\ 4 & 6 & 5 \\ 7 & 8 & 9 \end{pmatrix}$$ - A. 4 - B. 8 - C. 5 - D. 7 -
What is the correct term used to describe each individual number in a matrix?
- A. Dimension
- B. Element
- C. Row
- D. Column
-
Given the matrices
\begin{pmatrix} 3 & x & y \\ x & 7 & z \\ 6 & 4 & 2 \end{pmatrix} ,\quad N = \begin{pmatrix} 5 & 6 & y \\ 2 & x & z \\ 8 & 9 & 4 \end{pmatrix}$$ What is the value of $$x + y + z$$? - A. 12 - B. 16 - C. 18 - D. 22 -
Given that matrix
\begin{pmatrix} 3 & 7 \\ 2 & 5 \end{pmatrix} ,\quad H = \begin{pmatrix} 4 & 6 \\ 1 & 8 \end{pmatrix}$$ Find the value of $$G - H$$. - A. \(\begin{pmatrix} -1 & 1 \\ 1 & -3 \end{pmatrix}\) - B. \(\begin{pmatrix} -2 & 0 \\ 1 & -2 \end{pmatrix}\) - C. \(\begin{pmatrix} -1 & 1 \\ 1 & 3 \end{pmatrix}\) - D. \(\begin{pmatrix} -1 & -1 \\ 1 & -3 \end{pmatrix}\)
Do you need more details or have any questions?
Here are 5 related questions for deeper understanding:
- How do you determine the dimension of a matrix from its elements?
- What is the main difference between a row and a column in a matrix?
- Can a matrix have more than one inverse?
- What does the determinant of a matrix tell you about its invertibility?
- How is matrix addition different from matrix multiplication?
Tip: When multiplying matrices, ensure the number of columns in the first matrix equals the number of rows in the second for valid multiplication!
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Math Problem Analysis
Mathematical Concepts
Matrix
Matrix Dimensions
Matrix Elements
Matrix Operations
Formulas
Matrix dimensions: rows × columns
Matrix element notation: a_ij
Matrix subtraction and addition: A - B = C
Theorems
Inverse Matrix Theorem
Matrix Multiplication Rules
Suitable Grade Level
Grades 9-12