Home
Class 12
MATHS
If matrix A=[(1,-3,0)], then what is "AA...

If matrix `A=[(1,-3,0)]`, then what is `"AA'"` where `A'` is transpose of `A`.

A

`-10`

B

10

C

0

D

1

Text Solution

AI Generated Solution

The correct Answer is:
To find the product of the matrix \( A \) and its transpose \( A' \), we will follow these steps: 1. **Define the matrix \( A \)**: \[ A = \begin{pmatrix} 1 & -3 & 0 \end{pmatrix} \] Here, \( A \) is a row matrix with 1 row and 3 columns. 2. **Find the transpose of \( A \)**: The transpose of a matrix is obtained by converting rows into columns. Thus, the transpose \( A' \) will be: \[ A' = \begin{pmatrix} 1 \\ -3 \\ 0 \end{pmatrix} \] Now, \( A' \) is a column matrix with 3 rows and 1 column. 3. **Multiply \( A \) by \( A' \)**: To multiply \( A \) (1x3 matrix) by \( A' \) (3x1 matrix), we perform the following calculation: \[ AA' = \begin{pmatrix} 1 & -3 & 0 \end{pmatrix} \begin{pmatrix} 1 \\ -3 \\ 0 \end{pmatrix} \] The result of this multiplication will be a \( 1 \times 1 \) matrix (a single number). 4. **Calculate the product**: The multiplication is done as follows: \[ AA' = (1 \times 1) + (-3 \times -3) + (0 \times 0) \] \[ = 1 + 9 + 0 \] \[ = 10 \] 5. **Final result**: Therefore, the result of \( AA' \) is: \[ AA' = 10 \]
Promotional Banner

Similar Questions

Explore conceptually related problems

If A is a square matrix and |A|=2, then write the value of |AA'|, where A' is the transpose of matrix A

If matrix A=(1backslash2backslash3), ,write AA', where A' is the transpose of matrix A

If matrix A=[[1,2,3]], write AA^(T)

If A=[[2,1,3],[3,-2,1]] and B=[[1,-1],[0,2],[2,1]] , show that (AB)^'=B^'A^' where A^' is the transpose of A etc.

If A is a square matrix of order 2 and |A|=4 then find the value of |2AA'|, where A' is the transpose of matrix A.

A square matrix A is called orthogonal if Where A' is the transpose of A.

Consider the following statements 1. If A' = A, then A is a singular matrix, where A' is the transpose of A. 2. If A is a square matrix such that A^(3) = I , then A is non-singular. Which of the statements guven above is/are correct ?

If A is a 3xx3 matrix such that A^T = 5A + 2I , where A^T is the transpose of A and I is the 3xx3 identity matrix, then there exist a column matrix X=[[x],[y],[z]]!=[[0],[0],[0]] then AX is equal to

Let B=A^(3)-2A^(2)+3A-I where l is an identity matrix and A=[(1,3,2),(2,0,3),(1,-1,1)] then the transpose of matrix B is equal to