Advertisements
Advertisements
Question
The product of any matrix by the scalar ______ is the null matrix.
Advertisements
Solution
The product of any matrix by the scalar 0 is the null matrix.
Explanation:
The product of any matrix by the scalar 0' is the null matrix '0'.
i.e., 0 . A = 0
APPEARS IN
RELATED QUESTIONS
If `A = [(1, 2, -3),(5, 0, 2),(1, -1, 1)], B = [(3, -1, 2),(4, 2, 5),(2, 0, 3)] and C = [(4, 1, 2),(0, 3, 2),(1, -2, 3)]` then compute (A + B) and (B – C). Also verify that A + (B – C) = (A + B) – C.
If ` A = [(2/3, 1, 5/3),(1/3, 2/3, 4/3),(7/3, 2, 2/3)]` and `B = [(2/5, 3/5, 1),(1/5, 2/5, 4/5),(7/5, 6/5, 2/5)]`, then compute 3A – 5B.
Simplify `cos theta[(cos theta, sintheta),(-sin theta, cos theta)] + sin theta[(sin theta, -cos theta), (cos theta, sin theta)]`
Show that `[(5, -1),(6, 7)][(2, 1),(3, 4)] ≠ [(2, 1),(3, 4)][(5, -1),(6, 7)]`
Show that `[(1, 2, 3),(0, 1, 0),(1, 1, 0)][(-1, 1, 0),(0, -1, 1),(2, 3, 4)] ≠ [(-1, 1, 0),(0, -1, 1),(2, 3, 4)][(1, 2, 3),(0, 1, 0),(1, 1, 0)]`
Find A2 – 5A + 6I, if A = `[(2, 0, 1),(2, 1, 3),(1, -1, 0)]`
If A `= [(2"x", 0),("x","x")] "and A"^-1 = [(1,0),(-1,2)],` then x equals ____________.
If | A | = | kA |, where A is a square matrix of order 2, then sum of all possible values of k is ______.
What is scalar multiplication on matrices?
How is the negative of a matrix \[A\], denoted by \[-A\], defined?
If \[A=[a_{ij}]\], which matrix is \[-A\]?
What is the result of adding a matrix to its negative?
Which formula expresses distributive over matrix addition?
Which formula expresses distributive over scalar addition?
Which formula expresses associative with respect to scalar multiplication?
What is the result of multiplication by \[1\] for a matrix \[A\]?
What is the result of multiplication by \[0\] for a matrix \[A\]?
Which equality represents multiplication by the negative scalar \[-1\]?
Given \[2\begin{bmatrix}x&5\\7&y-3\end{bmatrix}+\begin{bmatrix}3&-4\\1&2\end{bmatrix}=\begin{bmatrix}7&6\\15&14\end{bmatrix}\], what is the value of \[x\]?
Given \[2\begin{bmatrix}x&5\\7&y-3\end{bmatrix}+\begin{bmatrix}3&-4\\1&2\end{bmatrix}=\begin{bmatrix}7&6\\15&14\end{bmatrix}\], what is the value of \[y\]?
After scalar multiplication and matrix addition, which matrix is equal to \[\begin{bmatrix}7&6\\15&14\end{bmatrix}\] in the given equation?
