Assume X,Y,Z,W and P are matrices of order 2 x n, 3 x k, 2 x p, n x 3, and p x k respectively.
The restriction on n, k and p so that PY+WY will be defined are:
A. k = 3,p = n
B. k is arbitrary, p = 2
C. p is arbitrary, k=3
D. k=2,p=3
Assume X,Y,Z,W and P are matrices of order 2 x n, 3 x k, 2 x p, n x 3, and p x k respectively.
The restriction on n, k and p so that PY+WY will be defined are:
A. k = 3,p = n
B. k is arbitrary, p = 2
C. p is arbitrary, k=3
D. k=2,p=3
Solution and Explanation
Matrices P and Y are of the orders p × k and 3 × k respectively.
Therefore, matrix PY will be defined if k = 3. Consequently,
PY will be of the order p × k. Matrices W and Y are of the orders n × 3 and 3 × k respectively.
Since the number of columns in W is equal to the number of rows in Y, matrix WY is
well-defined and is of the order n × k.
Matrices PY and WY can be added only when their orders are the same.
However, PY is of the order p × k and WY is of the order n × k. Therefore, we must have p = n.
Thus, k = 3 and p = n are the restrictions on n, k, and p so that will be defined.
Top Questions on Matrices
- If \( A \) is a square matrix of order \( 3 \times 3 \), \( \det A = 3 \), then the value of \( \det(3A^{-1}) \) is:
Three students, Neha, Rani, and Sam go to a market to purchase stationery items. Neha buys 4 pens, 3 notepads, and 2 erasers and pays ₹ 60. Rani buys 2 pens, 4 notepads, and 6 erasers for ₹ 90. Sam pays ₹ 70 for 6 pens, 2 notepads, and 3 erasers.
Based upon the above information, answer the following questions:(i) Form the equations required to solve the problem of finding the price of each item, and express it in the matrix form \( A \mathbf{X} = B \).
- If \[ A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & -2 \end{bmatrix}, \] then \( |A| \) is:
- If $A = \begin{bmatrix} 2 & 3 \\ -1 & 2 \end{bmatrix}$, then show that $A^2 - 4A + 7I = 0$.
- Let \( A = \begin{bmatrix} 1 & -2 & -1 \\ 0 & 4 & -1 \\ -3 & 2 & 1 \end{bmatrix}, B = \begin{bmatrix} -5 \\ -2 \end{bmatrix}, C = [9 \ \ 7], \) which of the following is defined?
Questions Asked in CBSE CLASS XII exam
- (b) If $2x^2 - 5xy + y^3 = 76$, then find $\frac{dy}{dx}$.
- CBSE CLASS XII - 2025
- Differentiation
- “If you want to test a man’s character, give him power.” Analyse the theme of The Tiger King in the light of the above quote. (The Tiger King)
- A coil has 100 turns, each of area \( 0.05 \, \text{m}^2 \) and total resistance \( 1.5 \, \Omega \). It is inserted at an instant in a magnetic field of \( 90 \, \text{mT} \), with its axis parallel to the field. The charge induced in the coil at that instant is:
- CBSE CLASS XII - 2025
- Electromagnetic induction
- A 1 cm segment of a wire lying along the x-axis carries a current of 0.5 A along the \( +x \)-direction. A magnetic field \( \vec{B} = (0.4 \, \text{mT} \hat{j}) + (0.6 \, \text{mT} \hat{k}) \) is switched on. The force acting on the segment is:
- CBSE CLASS XII - 2025
- Magnetic Force on a Current-Carrying Wire
- Two wires of the same material and the same radius have their lengths in the ratio 2:3. They are connected in parallel to a battery which supplies a current of 15 A. Find the current through the wires.
- CBSE CLASS XII - 2025
- Current electricity