Which of the following statements is true for the transpose of a matrix?
The number of rows is same as that of the given matrix.
The number of columns is same as that of the given matrix.
The order is same as that of the given matrix.
The number of elements is same as that of the given matrix.
Matrices
3 Likes

Question

Which of the following statements is true for the transpose of a matrix?
The number of rows is same as that of the given matrix.
The number of columns is same as that of the given matrix.
The order is same as that of the given matrix.
The number of elements is same as that of the given matrix.

Matrices

3 Likes

KnowledgeBoat · Accepted Answer

If A = m × n then AT = n × m The total number of elements is calculated by multiplying the dimensions: m × n. Since m × n = n × m Therefore, total number of elements in A is exactly the same as the total number of elements in AT Hence, option 4 is the correct option.

Mathematics

Which of the following statements is true for the transpose of a matrix?
The number of rows is same as that of the given matrix.
The number of columns is same as that of the given matrix.
The order is same as that of the given matrix.
The number of elements is same as that of the given matrix.

Matrices

Answer

Related Questions

If $\begin{bmatrix} 5 & 3 \ x & 7 \end{bmatrix} = \begin{bmatrix} y & z \ 1 & 7 \end{bmatrix}$ , then the value of (x + y + z) is:
9
8
11
10

If $\begin{bmatrix} x - y & 2x + z \ 2x - y & 3z + w \end{bmatrix} = \begin{bmatrix} -1 & 5 \ 0 & 13 \end{bmatrix}$ , then the value of (x + y + z + w) is:
8
9
10
12

If $\begin{bmatrix} x + y \ x - y \end{bmatrix} = \begin{bmatrix} 8 \ 4 \end{bmatrix}$ , then the value of xy is:
4
8
10
12

If $\begin{bmatrix} p - q & 2q \ 2q + r & p + q \end{bmatrix} = \begin{bmatrix} 1 & 4 \ 9 & 5 \end{bmatrix}$ , then the value of (p + q + r) is:
8
10
-5
-10

Mathematics

Which of the following statements is true for the transpose of a matrix?The number of rows is same as that of the given matrix.The number of columns is same as that of the given matrix.The order is same as that of the given matrix.The number of elements is same as that of the given matrix.

Matrices

Answer

Related Questions

If [53x7]=[yz17]\begin{bmatrix} 5 & 3 \ x & 7 \end{bmatrix} = \begin{bmatrix} y & z \ 1 & 7 \end{bmatrix}[5x​37​]=[y1​z7​], then the value of (x + y + z) is:981110

If [x−y2x+z2x−y3z+w]=[−15013]\begin{bmatrix} x - y & 2x + z \ 2x - y & 3z + w \end{bmatrix} = \begin{bmatrix} -1 & 5 \ 0 & 13 \end{bmatrix}[x−y2x−y​2x+z3z+w​]=[−10​513​], then the value of (x + y + z + w) is:891012

If [x+yx−y]=[84]\begin{bmatrix} x + y \ x - y \end{bmatrix} = \begin{bmatrix} 8 \ 4 \end{bmatrix}[x+yx−y​]=[84​], then the value of xy is:481012

If [p−q2q2q+rp+q]=[1495]\begin{bmatrix} p - q & 2q \ 2q + r & p + q \end{bmatrix} = \begin{bmatrix} 1 & 4 \ 9 & 5 \end{bmatrix}[p−q2q+r​2qp+q​]=[19​45​], then the value of (p + q + r) is:810-5-10

Which of the following statements is true for the transpose of a matrix?
The number of rows is same as that of the given matrix.
The number of columns is same as that of the given matrix.
The order is same as that of the given matrix.
The number of elements is same as that of the given matrix.

If $\begin{bmatrix} 5 & 3 \ x & 7 \end{bmatrix} = \begin{bmatrix} y & z \ 1 & 7 \end{bmatrix}$ , then the value of (x + y + z) is:
9
8
11
10

If $\begin{bmatrix} x - y & 2x + z \ 2x - y & 3z + w \end{bmatrix} = \begin{bmatrix} -1 & 5 \ 0 & 13 \end{bmatrix}$ , then the value of (x + y + z + w) is:
8
9
10
12

If $\begin{bmatrix} x + y \ x - y \end{bmatrix} = \begin{bmatrix} 8 \ 4 \end{bmatrix}$ , then the value of xy is:
4
8
10
12

If $\begin{bmatrix} p - q & 2q \ 2q + r & p + q \end{bmatrix} = \begin{bmatrix} 1 & 4 \ 9 & 5 \end{bmatrix}$ , then the value of (p + q + r) is:
8
10
-5
-10