Video: ο»Ώ Determining Whether Two Matrices Are Equal

Given that 𝐴 = [βˆ’0.6, βˆ’1/2, and βˆ’7/10, 1], 𝐡 = βˆ’3/5, βˆ’0.5, and βˆ’0.7, 1], is it true that 𝐴 = 𝐡?

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Video Transcript

Given that 𝐴 is the matrix negative 0.6, negative a half, negative seven over 10, one, and 𝐡 is the matrix negative three over five, negative 0.5, negative 0.7, and one, is it true that 𝐴 is equal to 𝐡?

Well, for 𝐴 to be equal to 𝐡, then what we need to do is have a look at the individual elements because the corresponding elements in each of our matrices would have to be the same. So we can start with our first element. So we’ve got negative 0.6 or negative three over five. Well, negative 0.6 is equal to negative six over 10. Well, if we divide both the numerator and denominator by two, this is gonna give us negative three over five. So therefore, we can say that these elements are the same. So now let’s move on to our next element.

Well, if we take a look at our next element, we’ve got negative a half in our matrix 𝐴 and negative 0.5 in matrix 𝐡. Well, negative a half is the same as, it’s equal to, negative 0.5. So these elements are also the same. And then looking at the next element, we’ve got negative seven over 10 or seven-tenths and negative 0.7. Well, the first decimal is tenths, so negative 0.7 is the same as negative seven-tenths. So these elements are the same. And then the final element is just one in each of our matrices. So therefore, we can say that it is true, yes, that 𝐴 is equal to 𝐡.

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